Waveguide coating optimization

Abstract

A method of forming a transmissive coating for a waveguide. The transmissive coating includes a plurality of layers. The method comprises the step a of determining a first coating parameter and a coating function for each layer to optimize transmissivity at a plurality of locations along the waveguide for a plurality of different wavelengths. The coating function is selected from a plurality of allowable coating functions. Subsequently, step b: forming a plurality of layers using the determined coating parameters and coating functions. And then a step c of measuring the thickness of at least one layer at each of the plurality of positions. The measurement indicates that the coating function deviates from the function selected during the optimization of step a. Finally, step d: determining a second coating parameter of the at least one layer by repeating the optimization of step a using a coating function derived from the measurements of step c.

Description

Technical Field

[0001] The present disclosure relates to pupil expansion or wavefront replication. More specifically, the present disclosure relates to waveguides, display systems including at least one waveguide according to the present disclosure, methods for wavefront replication using at least one waveguide, and methods for waveguide wavefronts, such as holographic wavefronts. Still more specifically, the present disclosure relates to methods for improving the uniformity of a replica of a wavefront output by a waveguide and optical components therefor (e.g., optical layers, dielectric layers, or dielectric stacks). The present disclosure also relates to methods for forming a transmissive coating for a waveguide, methods for designing a transmissive coating for a waveguide, and methods for manufacturing a transmissive coating for a waveguide. The transmissive coating may be a graded transmissive coating. Background Art

[0002] Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured, for example, on a photographic plate using well-known interference techniques to form a holographic recording or "hologram" consisting of interference fringes. The hologram can be reconstructed by illuminating it with appropriate light to form a two- or three-dimensional holographic reconstruction or replay image representing the original object.

[0003] Computer-generated holography can numerically simulate interference processes. Computer-generated holograms can be computed using techniques based on mathematical transformations such as the Fresnel or Fourier transforms. These types of holograms are referred to as Fresnel / Fourier transform holograms or simply Fresnel / Fourier holograms. Fourier holograms can be considered either Fourier domain / planar representations of an object or frequency domain / planar representations of an object. Computer-generated holograms can also be computed, for example, using coherent ray tracing or point cloud techniques.

[0004] The computer generated hologram may be encoded on a spatial light modulator arranged to modulate the amplitude and / or phase of the incident light. For example, light modulation may be achieved using electrically addressable liquid crystals, optically addressable liquid crystals, or micromirrors.

[0005] A spatial light modulator typically comprises a plurality of individually addressable pixels, which may also be referred to as cells or elements. The light modulation scheme may be binary, multi-level, or continuous. Alternatively, the device may be continuous (i.e., comprise no pixels), so that the light modulation may be continuous across the device. A spatial light modulator may be reflective, meaning that the light is modulated to reflect the output. A spatial light modulator may also be transmissive, meaning that the light is modulated to transmit the output.

[0006] The system described here can be used to provide a holographic projector, which has already been used, for example, in head-up displays (HUDs). Summary of the Invention

[0007] Aspects of the present disclosure are defined in the accompanying independent claims.

[0008] Broadly, the present disclosure relates to image projection. It relates to a method of image projection and an image projector including a display device. The present disclosure also relates to a projection system including an image projector and an observation system, wherein the image projector projects or relays light from the display device to the observation system. The present disclosure is equally applicable to monocular and binocular observation systems. The observation system may include one or more eyes of an observer. The observation system includes an optical element having optical power (e.g., the lens of a human eye) and an observation plane (e.g., the retina of a human eye). The projector may be referred to as a "light engine." The display device and the image formed (or perceived) using the display device are spatially separated from each other. The observer forms or perceives the image on the display plane. In some embodiments, the image is a virtual image, and the display plane may be referred to as a virtual image plane. In other embodiments, the image is a real image formed by holographic reconstruction, and the image is projected or relayed to the observation plane. The image is formed by illuminating a diffraction pattern (e.g., a hologram) displayed on the display device.

[0009] A display device includes pixels. The pixels of the display device diffract light. According to well-known optical principles, the magnitude of the maximum diffraction angle depends on the size of the pixel (and other factors, such as the wavelength of the light).

[0010] In an embodiment, the display device is a spatial light modulator, such as a liquid crystal on silicon ("LCOS") spatial light modulator (SLM). Light is transmitted from the LCOS to a viewing entity / system, such as a camera or an eye, over a range of diffraction angles (e.g., from zero to a maximum diffraction angle). In some embodiments, amplification techniques can be used to increase the range of available diffraction angles beyond the conventional maximum diffraction angle of the LCOS.

[0011] In some examples, the image (formed by the displayed hologram) is propagated to the eye. For example, spatially modulated light of an intermediate holographic reconstruction / image formed in free space or on a screen or other light receiving surface between the display device and the observer can be propagated to the observer.

[0012] In some other examples, the hologram itself (the light) is transmitted to the eye. For example, the spatially modulated light of the hologram (not yet fully converted into a holographic reconstruction, i.e., an image) - which can be informally referred to as being "encoded with / by the hologram" - is transmitted directly to the observer's eye. The observer can perceive a real or virtual image. In these embodiments, no intermediate holographic reconstruction / image is formed between the display device and the observer. It is sometimes said that in these embodiments, the lens of the eye performs the conversion or transformation of the hologram into the image. The projection system or light engine can be configured so that the observer effectively looks directly into the display device.

[0013] According to well-known optical principles, the angular range of light propagating from a display device that can be observed by an eye or other observing entity / system varies with the distance between the display device and the observing entity. For example, at a viewing distance of 1 meter, only a small range of angles of light from an LCOS can propagate through the pupil of the eye to form an image on the retina at a given eye position. The angular range of light propagating from the display device that can successfully propagate through the pupil of the eye to form an image on the retina at a given eye position determines the portion of the image that is "visible" to the observer. In other words, not all portions of the image are visible from any one point on the viewing plane (e.g., any one eye position within an observation window such as an eye box).

[0014] In some embodiments, the image perceived by the observer is a virtual image that appears upstream from the display device—that is, the observer perceives the image as being farther away from them than the display device. Thus, conceptually, the observer can be thought of as viewing the virtual image through a "display-sized window," which can be very small, such as 1 cm in diameter, at a relatively large distance, such as 1 meter. Furthermore, the user will be viewing the display-sized window through their eye's pupil, which can also be very small. Consequently, the field of view is reduced at any given time, and the specific angular range that can be seen is heavily dependent on eye position.

[0015] Pupil expanders address how to increase the angular range of light rays propagating from a display device so that they can successfully propagate through the pupil of the eye to form an image. Display devices are typically (relatively) small and have a (relatively) large projection distance. In some embodiments, the projection distance is at least an order of magnitude, for example, at least two orders of magnitude, greater than the diameter or width of the display device's entrance pupil and / or aperture (i.e., the size of the pixel array).

[0016] The use of a pupil expander laterally increases the viewing area (i.e., the user's eyebox), thereby enabling some eye movement while still allowing the user to see the image. As will be understood by those skilled in the art, in an imaging system, the viewing area (the user's eyebox) is the area within which the viewer's eye can perceive the image. The present disclosure relates particularly to non-infinite virtual image distances—i.e., near-field virtual images—but is equally applicable to virtual images formed at infinity or even real images formed downstream of a display device / hologram.

[0017] The display device can have an active or pixel display area having a first dimension of less than 10 cm, such as less than 5 cm or less than 2 cm. The propagation distance between the display device and the viewing system can be greater than 1 m, such as greater than 1.5 m or greater than 2 m. The optical propagation distance within the waveguide can be up to 2 m, such as up to 1.5 m or up to 1 m. The method can receive an image and determine a corresponding hologram of sufficient quality within a range of less than 20 m, such as less than 15 m or less than 10 m.

[0018] In some embodiments—described solely by way of example using diffractive or holographic light fields or wavefronts according to the present disclosure—a hologram is configured to route light into multiple channels, each corresponding to a different portion (i.e., subregion) of an image. The hologram can be presented on a display device, such as a spatial light modulator, such as a display. When displayed on an appropriate display device, the hologram can spatially modulate light that can be converted into an image by an observation system. The channels formed by the diffractive structure are referred to herein as "hologram channels" simply to reflect that they are channels of light encoded by the hologram with image information. The light of each channel can be said to be in the holographic domain, rather than in the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram, and thus the hologram domain is the Fourier or frequency domain. The hologram can also be a Fresnel or Fresnel transform hologram. The hologram is described herein as routing light into multiple hologram channels simply to reflect that the image reconstructible from the hologram has a finite size and can be arbitrarily divided into multiple image subregions, where each hologram channel will correspond to each image subregion. Importantly, the hologram of this example is characterized by how it distributes the image content when illuminated. Specifically, the hologram divides the image content by angle. That is, every point on the image is associated with a unique ray angle in the spatially modulated light formed by the hologram when illuminated - at least a unique pair of angles, because the hologram is two-dimensional. For the avoidance of doubt, this holographic behavior is not conventional. When illuminated, the spatially modulated light formed by this particular type of hologram can be arbitrarily divided into multiple hologram channels, where each hologram channel is defined by a range of ray angles (in two dimensions). It will be understood from the above that any hologram channel (i.e., a sub-range of ray angles) that can be considered in the spatially modulated light will be associated with a corresponding part or sub-region of the image. That is, all the information required to reconstruct that part or sub-region of the image is contained within the angular sub-range of the spatially modulated light formed by the hologram of the image. When the spatially modulated light is observed as a whole, there is not necessarily any evidence of multiple discrete light channels. However, in some arrangements, multiple spatially separated hologram channels are formed by intentionally leaving areas of the target image from which the hologram is calculated blank or empty (ie, without image content).

[0019] Despite this, the hologram can still be recognized. For example, if only a continuous portion or subregion of the spatially modulated light formed by the hologram is reconstructed, only a subregion of the image should be visible. If a different continuous portion or subregion of the spatially modulated light is reconstructed, a different subregion of the image should be visible. Another identifying feature of this type of hologram is that the shape of the cross-section of any hologram channel substantially corresponds to (i.e., is substantially identical to) the shape of the entrance pupil, although the size may differ—at least at the correct plane from which the hologram was calculated. Each light / hologram channel propagates from the hologram at a different angle or range of angles. While these are example ways to characterize or identify this type of hologram, other approaches may also be used. In summary, the holograms disclosed herein are characterized and identified by how the image content is distributed within the light encoded by the hologram. Furthermore, for the avoidance of doubt, references herein to holograms configured to direct light or angularly divide an image into multiple hologram channels are by way of example only, and the present disclosure is equally applicable to pupil expansion of any type of wavefront or light field, including any type of diffraction or diffracted light field.

[0020] In summary, disclosed herein is a system for providing pupil expansion for an input light field or wavefront, wherein the input light field is optionally a diffracted or holographic light field comprising a diverging light beam. As described above, pupil expansion (which may also be referred to as "image replication," "replication," or "pupil replication") increases the size of the region in which an observer can see an image (or in which a hologram's light is received, with the observer's eye forming the image) by creating one or more replicas of the input light (or light beam). Pupil expansion can be provided in one or more dimensions. For example, two-dimensional pupil expansion can be provided, where each dimension is substantially orthogonal to a corresponding other dimension. In embodiments where the wavefront is a holographic wavefront, the process can be described as hologram replication.

[0021] The system can be provided in a compact and streamlined physical form. This makes the system suitable for a wide range of practical applications, including those where space is limited and asset value is high. For example, it can be implemented in a head-up display (HUD), such as a vehicle or automotive HUD.

[0022] In this disclosure, the term "replica" is used solely to reflect the fact that spatially modulated light is split, resulting in a composite light field or wavefront being directed along multiple distinct optical paths. The term "replica" is used to refer to each occurrence or instance of the composite light field or wavefront following a replication event—such as the partial reflection-transmission of a pupil expander. Each replica propagates along a different optical path. Some embodiments of the present disclosure relate to the propagation of light encoded with a hologram rather than an image—that is, light spatially modulated with a hologram of an image rather than the image itself. Those skilled in the art of holography will understand that the composite light field associated with the propagation of light encoded with a hologram will vary with propagation distance. The term "replica" as used herein is independent of propagation distance, so two light branches or paths associated with a replication event are still referred to as "replicas" of each other, even if the branches have different lengths, causing the composite light field to evolve differently along each path. That is, according to this disclosure, even if two composite light fields are associated with different propagation distances, they are still considered "replicas"—assuming they originate from the same replication event or series of replication events.

[0023] As described above, an optical waveguide used as a pupil expander can guide light or a light field or wavefront between a pair of parallel surfaces. This can be achieved through internal reflections between the parallel surfaces. The first surface in the pair can be partially transmissive-reflective. The second surface in the pair can be reflective. Thus, the light field is split at each internal reflection at the first surface, so that multiple copies of the light field are transmitted through the region of the first surface that forms the waveguide output port. Thus, the observation window (and eye box) is enlarged by the waveguide.

[0024] It is desired that the intensity and spectrum of each successive replica emitted by the waveguide be substantially constant across the replicas. For example, the integral of the light intensity of each replica may be substantially constant, the average of the light intensity of each replica may be substantially constant, and / or the distribution of the light intensity of each replica may be substantially constant. Replicas having substantially constant intensity and spectrum are referred to herein as spatially uniform, and a waveguide emitting such replicas is referred to herein as providing spatially uniform emission. Spatially uniform replicas advantageously reduce or minimize the variability in the brightness of the image (or different regions thereof) perceived by an observer moving around the (extended) viewing window. Furthermore, the overall quality of the hologram received by the observer (and / or the final image perceived by the observer) may be improved, particularly if the hologram comprises light of multiple different wavelengths.

[0025] The intensity of light guided between the first and second surfaces of a waveguide will decrease after each division of the light field at the first surface. Suboptimal waveguides can often include a first surface with constant reflectivity. This results in a decrease in intensity with each successive replica. In other words, such conventional waveguides do not provide spatially uniform emission.

[0026] A graded coating can be applied to a waveguide to provide a first surface with different reflectivities, and therefore different transmittances. In particular, the coating can be arranged so that the transmittance of the first surface increases in the waveguide direction. The graded coating can be arranged so that the increase in transmittance of the first surface in the waveguide direction accounts for (e.g., at least partially compensates for) a decrease in the intensity of the light (being guided). However, current graded coatings often result in high absorption losses in the waveguided light. Furthermore, these coatings typically allow very limited control over the spectral properties, which is particularly disadvantageous when the light being waveguided comprises multiple wavelengths. While some improved graded coatings are available, these coatings are expensive, time-consuming, and complex to manufacture, and are generally not reliably manufactured. For example, such a coating may include multiple layers (typically 20 or more) of dielectric material, each layer having a unique thickness percentage variation from a first end to a second end of the layer. Such a complex layered structure may be necessary to provide substantially spatially uniform emission across the entire visible spectrum, but is slow to manufacture and difficult to reliably produce (e.g., may require a mobile grader to be present in the coating chamber).

[0027] The present disclosure addresses the technical problem of providing spatially uniform emission from a waveguide pupil expander, such that the intensity and spectrum of each replica are substantially similar. The present disclosure provides an improved waveguide pupil expander that provides substantially uniform emission at least at specific wavelengths, such as red, green, and blue wavelengths. The first surface of the waveguide includes a plurality of alternating layers of first and second dielectric materials having different refractive indices. Instead of each layer having a unique thickness percentage variation, in the present disclosure, each dielectric layer has a thickness percentage variation that is one of a discrete number of values, the number of discrete values ​​being less than the total number of layers. In some embodiments, the number of discrete or allowable values ​​is no more than four. In some embodiments, the number of layers is at least twice the number of discrete values.

[0028] The multilayer structures obtained by conventional design techniques are very complex and not suitable for industrial scale-up. The complexity is partly due to the need to achieve uniformity at three different wavelengths. The design process has been rethought and focused on restricting it in ways that simplify the required manufacturing method and relaxing it in other ways that do not affect the image forming (e.g. holographic) process. In particular, emphasis has been placed on how the required coating machine can be simplified. If the number of different gradients used in the stack is restricted (e.g. reduced to fewer than five or even fewer than four or three) and degrees of freedom are introduced for intermediate wavelengths (e.g. wavelengths between the three hologram wavelengths), sufficient optical performance for three-color hologram replication can still be achieved. Because the number of different grading tools is reduced, the manufacturing costs are significantly reduced.

[0029] Compared to conventional methods required to produce stacks, faster and more reliable manufacturing methods can be used to produce the stacks of the present invention, in which each layer has a unique thickness percentage variation. By limiting the design of the waveguide coating to only consider specific regions of the visible spectrum, such alternating stacks according to the present disclosure can be arranged to provide desired optical properties, such as spatially uniform emission and low absorption losses at these wavelengths (but not necessarily at other wavelengths). In this way, the waveguides of the present disclosure may be particularly suitable for applications where specific wavelengths of light are to be waveguided rather than the full spectrum. For example, in many applications, spatially uniform emission of red, green and / or blue light from a waveguide may be desired, but other wavelengths (e.g., in the yellow region of the spectrum) may not be desired. Such applications include head-up displays. The waveguides of the present disclosure may be suitable for such applications. As will be understood by those skilled in the art, full-color images can be generated using red, green and blue light.

[0030] According to a first example, a waveguide is provided. The waveguide includes a pair of parallel / complementary surfaces arranged to provide a waveguide therebetween. A first surface of the pair of parallel surfaces includes multiple layers of a first dielectric and multiple layers of a second dielectric arranged in an alternating configuration.

[0031] Each layer of the first and second dielectrics has a first end and a second end. The first end can be a (light) input end, and the second end can be a (light) output end or an end of an output port / window of a final replica. The percentage change in thickness of each layer from the first end to the second end of the layer has one of a plurality of discrete (e.g., allowable) values. The total number of layers of the first and second dielectrics is greater than the total number of discrete values. The difference in refractive index between the first and second dielectrics is greater than 0.4, and optionally greater than 0.5.

[0032] Unless otherwise specified, the "percent change in thickness" of a layer referred to herein refers to the percent change in thickness of the layer from a first end of the layer to a second end of the layer. The percent change in thickness of a layer can be: 100×(t f –t i ) / t i , where t i is the thickness of the corresponding layer at the first end, t f is the thickness of the corresponding layer at the second end.

[0033] Typically, each of the plurality of layers can be parallel to the other layers. The first end of each layer can be aligned with the first end of the other layers, and the second end of each layer can be aligned with the other layers. In other words, each layer can have a substantially similar length and / or width as the other layers, but can have a different thickness or depth. The plurality of layers of first and second dielectrics can be referred to as a stack, or simply a dielectric stack.

[0034] As used herein, an "alternating arrangement" of first and second dielectric layers means that each layer of the first dielectric is separated from the next closest layer of the first dielectric by a second dielectric layer, and vice versa.

[0035] As used herein, a plurality of discrete values ​​means a plurality of values ​​that are different from one another. In other words, no single discrete value in the plurality of discrete values ​​is identical to any other discrete value. Each discrete value may differ in magnitude and / or polarity. The discrete values ​​may be referred to as "allowable" or "predetermined" values. The thickness variation rate of each layer may be selected or determined during the manufacturing process. For example, if the plurality of layers of the first surface of the waveguide are formed or manufactured using a shadow mask, the thickness variation rate of each layer may be related to the shape of the shadow mask, such that each discrete value is associated with a corresponding shadow mask. Those skilled in the art will appreciate that the "allowable" or "predetermined" discrete values ​​may take any suitable value that provides the desired optical properties for a particular multilayer structure of first and second dielectrics, and that suitable values ​​may be calculated or determined, for example, using simulations. Each discrete value may be positive or negative. A positive value indicates that the thickness increases from the first end to the second end, while a negative value indicates that the thickness decreases from the first end to the second end.

[0036] The percent change in thickness of each layer is equal to one of the plurality of discrete values. Because there are more layers than discrete values, at least two layers have the same percent change in thickness from the respective first end to the respective second end. In some embodiments, more than two layers, optionally four or more layers, optionally six or more layers, optionally eight or more layers, optionally ten or more layers in the plurality of layers may have the same percent change in thickness from the respective first end to the respective second end (thus, these layers may be associated with the same discrete value). In some embodiments, the layers having the same percent change in thickness are layers of the same dielectric (i.e., all layers having a particular percent change in thickness value are either the first dielectric layer or the second dielectric layer).

[0037] Each of the first or second dielectric layers can increase or decrease in thickness in the waveguiding direction. A first direction can be defined from the first end to the second end of each of the plurality of layers. The pair of parallel surfaces can be arranged to provide waveguiding in the first direction. In other words, light waveguided by the pair of surfaces can interact with the first end before interacting with the second end. Furthermore, each of the first or second dielectric layers can increase or decrease in thickness in the first direction.

[0038] The minimum thickness of each of the multiple layers of the first and second dielectrics, as well as discrete values ​​for the percentage variation in thickness, can be selected to provide a waveguide with desired optical properties, in particular with desired transmission behavior, resulting in spatially uniform emission. The parameters may depend on, among other things, the material properties of the first and second dielectrics (in particular the refractive index), the angle of incidence of the light entering the waveguide, the wavelength of the incident light, and the distance between the pair of parallel surfaces of the waveguide. As will be appreciated by those skilled in the art, there will be multiple (usually relatively large) arrangements of multiple layers to provide a waveguide with desired optical properties. However, a common advantage of all of these arrangements is that the layered structure of the first surface provides the desired optical properties and can be manufactured quickly, cheaply, and reliably.

[0039] One example of a fast, inexpensive, and reliable method for fabricating the first and second dielectric layers can include forming the layers by depositing the respective dielectric materials onto a waveguide substrate. A shadow mask can be used to control the flow of the dielectric material onto the substrate. Preferably, a shadow mask having a trapezoidal shape can be used. The percentage variation in thickness of each layer can be determined by the shape of the shadow mask, and the total thickness of each layer can be determined by the length of time the dielectric material is allowed to flow. When the shadow mask is trapezoidal, the percentage variation in thickness of each layer can correspond to the percentage variation of the short side to the long side of the trapezoidal shape of the shadow mask. A different shadow mask can be associated with each discrete value. For example, if there are first to fourth percentage variation values, four different shadow masks can be used to fabricate each layer of the coating. Advantageously, the waveguide substrate can be easily moved between different material sources with different shadow masks.

[0040] The plurality of discrete values ​​may include or consist of two or more discrete (allowable) values, optionally three or more (allowable) discrete values, optionally four or more (allowable) values. The plurality of discrete values ​​may consist of two to six discrete values, optionally two to four discrete values, optionally four discrete values. The number of discrete values ​​may preferably be significantly lower than the total number of layers. For example, in some embodiments, the total number of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers.

[0041] The plurality of discrete values ​​may include a first value, a second value, and a third value. Each layer of the first dielectric may have a thickness percentage variation equal to the first value or the second value. In other words, there may be only two options for the thickness percentage variation of each layer of the first dielectric.

[0042] At least one layer of the second dielectric may have a thickness percentage variation equal to the third value. When each layer of the first dielectric has the first discrete value or the second discrete value, this may mean that at least one layer of the second dielectric has a different thickness percentage variation relative to all layers of the first dielectric.

[0043] In addition to the first to third values, the plurality of discrete values ​​may include a fourth value. Each layer of the second dielectric may have a thickness percentage variation equal to the third value or the fourth value. In other words, there may be only two options for the thickness percentage variation of each layer of the second dielectric. When each layer of the first dielectric has the first discrete value or the second discrete value, this may mean that each layer of the second dielectric has a different thickness percentage relative to all layers of the first dielectric.

[0044] Preferably, the thickness variation rate of each layer of the first and second dielectrics can be constant. In other words, each layer can have a linear profile. Manufacturing dielectric layers with linear profiles can be simpler. Furthermore, those skilled in the art will appreciate that calculating / determining the discrete allowable values ​​for stacks with linear profiles can be simpler.

[0045] In some embodiments, the first surface can provide a plurality of (n) light emission zones for light waveguided between the first surface and the second surface. The plurality of light emission zones can be distributed along the length of the first surface in the waveguide direction. A replica of the input wavefront can be generated in each emission zone. The first end of each of the first and second dielectric layers can be at or adjacent to the first light emission zone. The second end of each of the first and second dielectric layers can be at or adjacent to the nth light emission zone.

[0046] The internal incident angle of each emission region may be in the range of 0 to 70 degrees, preferably in the range of 10 to 50 degrees.

[0047] At other wavelengths (i.e., not the first, second, and third visible wavelengths), the transmittance of the first surface may or may not increase in the waveguide direction. As previously discussed, the waveguide of the present disclosure may be particularly advantageous in situations where light is waveguided at discrete wavelengths rather than being waveguided to have a continuous spectrum. The inventors have recognized that parameters, such as the thickness and percentage thickness variation of the multiple layers of the first and second dielectrics, can be selected to provide the desired varying transmittance behavior only at the first, second, and third wavelengths, and that it may not be necessary for the layers to provide the same transmittance behavior at other wavelengths. The inventors have discovered that by limiting the problem of providing varying transmittance behavior to only certain wavelengths, a coating comprising multiple layers having the same thickness variation can provide the desired transmittance behavior, which, as described above, can be manufactured cheaply, quickly, and reliably while still providing acceptable transmission characteristics.

[0048] The first wavelength mentioned above may preferably be within the range of 630-670 nm. The second wavelength may preferably be within the range of 500-540 nm. The third wavelength may preferably be within the range of 430-470 nm. In other words, the first wavelength may correspond to red visible light. The second wavelength may correspond to green visible light. The third wavelength may correspond to blue visible light.

[0049] Preferably, the transmittance T(n) of the first surface at each emission point may satisfy the following equation: T(n) = (T(n-1)) / ([1-T(n-1)]×[1-L]), where L is the optical loss factor of the waveguide material.

[0050] The first dielectric may be a first oxide, fluoride, sulfide, or nitrate of a first transition metal or semiconductor. The second dielectric may be a second oxide, fluoride, sulfide, or nitrate of a second transition metal or semiconductor. In some embodiments, the first dielectric comprises silicon, titanium, tantalum, or hafnium. In some embodiments, the second dielectric comprises another of silicon, titanium, tantalum, or hafnium.

[0051] The thickness of each layer can be in the range of 2 to 300 nm. At any point between the first end and the second end, the thickness of each layer cannot exceed this range. In some embodiments, each layer can have a thickness in the range of 20 to 300 nm.

[0052] The minimum thickness of each layer can be between 2 and 300 nm, optionally between 20 and 300 nm. The maximum thickness of each layer can be between 2 and 300 nm, optionally between 20 and 300 nm. The minimum thickness of each layer is less than the maximum thickness of the corresponding layer. The minimum or maximum thickness of each layer can be at a first end of the layer. The other of the minimum or maximum thickness of the corresponding layer can be at a second end of the layer.

[0053] At least one of the plurality of discrete values ​​of the percent change in thickness may be positive.At least one of the plurality of discrete values ​​of the percent change in thickness may be negative.

[0054] Each of the plurality of discrete values ​​of the percent thickness change may be within the range of -150% to +150%.

[0055] The number of layers of the plurality of layers may be at least 10 layers, optionally at least 15 layers, optionally at least 20 layers. The number of layers of the plurality of layers may be in the range of 10 to 30 layers, optionally 15-25 layers.

[0056] According to a first aspect, a method for forming a transmissive coating for a waveguide is provided. The transmissive coating comprises a plurality of layers. The method comprises step a: determining first coating parameters and a coating function for each layer to optimize transmittance at a plurality of locations along the waveguide for a plurality of different wavelengths. The coating function is selected from a plurality of permissible coating functions. Next, step b: forming the plurality of layers using the determined coating parameters and coating function. Then, step c: measuring the thickness of at least one layer at each of the plurality of locations. The measurements indicate that the coating function deviates from the function selected during the optimization in step a. Finally, step d: determining second coating parameters for the at least one layer by repeating the optimization in step a using the coating function derived from the measurements in step c. Notably, the coating function is not adjusted. That is, step d retains the coating function determined in step a.

[0057] This optimization improves graded coating performance by adjusting the thickness of multiple layers without changing the gradient (shadow mask). It provides greater tolerance for the actual thickness gradient (linearity and amplitude), and thus for the shadow mask geometry. This reduces process development and prototyping time through fewer shadow mask iterations. The method also corrects for any residual variations in the shadow mask over time, especially in large-scale production, to continuously maintain yields in an automated feedback process.

[0058] In other words, a method for designing or manufacturing a transmissive coating for a waveguide is disclosed herein. The transmissive coating comprises a plurality of layers. The method comprises selecting, for each layer, (first) coating parameters and a (first) coating function from a plurality of permissible coating functions to optimize transmittance at a plurality of locations of the waveguide for a plurality of different wavelengths. The method comprises forming the plurality of layers using the determined coating parameters and coating function. The method further comprises measuring the thickness of the first layer at a plurality of locations, wherein the measurements indicate that the coating function deviates from the coating function selected during optimization. The method is characterized in that different (second) coating parameters are selected for at least one layer (e.g., the first layer and / or a different layer) by repeating the optimization using a (second) coating function derived from the measurements.

[0059] However, in practice, it is very difficult and time-consuming to adjust the shadow mask to the exact same gradient as designed. In large-scale production, the gradient may also change from time to time as the shadow mask degrades. In general, the present disclosure describes an optimization method that helps compensate for residual variations in gradient and improves the yield and optical performance of graded coatings. More specifically, this article discloses a method for designing a multilayer achromatic graded transmission coating using four linear gradients. Each gradient translates into a fixed geometry of a shadow mask of a single dielectric material. During the coating process, the gradient shadow mask physically blocks some material from being deposited on the substrate, thereby producing a gradient layer thickness of that material. By carefully combining multiple gradients plus multiple materials plus multiple layers, an optimized coating structure can meet the requirements of spatially graded transmission in the RGB window.

[0060] Typically, the thickness of the coating can be measured in situ or after coating to verify the parameters of the coating, particularly the thickness profile. If the measurements indicate that the coated mask no longer provides the desired performance, it is replaced. Thus, this is a binary pass or fail test, and it is accepted in the art that coated masks degrade over time and require replacement (i.e., they periodically "fail"). In industrial or high-volume applications, the process of stopping the production line, replacing the coated mask, and then restarting the manufacturing process is expensive in terms of time and cost. The inventors recognized that additional tolerances can be achieved by using pass or fail thickness verification measurements to determine the "actual" coating function of the mask. In summary, the method of the present invention includes identifying a coating function (which is a property or parameter of the physical coated mask) and a coating parameter (which is a parameter selected by the user, such as coating speed) for each layer. The inventors recognized that additional tolerances in mask performance (i.e., variations in a particular coating function) can be achieved by using the degrees of freedom associated with the coating parameters to compensate for degradation of the coating function. In this way, a method is provided that can compensate for wear of the components used to apply the coating (such as wear on the apertures of the shadow mask as described above), which can lead to inaccurate application of the layer, resulting in optical properties that differ from the desired ones. Step a) sets an initial set of values ​​that, under ideal conditions (i.e., no wear on the layer application / coating equipment), produce an optimized transmittance along the entire length (and optionally the width) of the waveguide. These values ​​can be generated by simulation, experimentation, or any other suitable method known to those skilled in the art. This can be referred to as a first optimization.

[0061] Step b then forms these layers, which can be done using the method described above. If there is no wear on the application equipment, there is no need to continue the method. However, this is not the case in reality, as is demonstrated in step c, where the resulting layer thickness is compared with the optimized (ideal) value determined in step a.

[0062] A second optimization (or re-optimization) is performed. The second optimization is similar to the first optimization, but uses a coating function determined by measurement rather than a specified / expected coating function for the shadow mask. In other words, the thickness of a layer (or each layer) is measured at multiple locations, and a second (measured) coating function is determined that deviates from the first (expected) coating function. A second optimization is then performed to identify second coating parameters. In other words, after the re-optimization (or second optimization) occurs, the second coating parameters are new or updated versions of the first coating parameters.

[0063] Significantly, the inventors have recognized that by performing a second optimization using a coating function determined by measurement (i.e., pass / fail testing) and adjusting selected coating parameters (e.g., coating speed), a certain degree of imperfections in the shadow mask can be tolerated. In other words, the inventors surprisingly discovered that the degrees of freedom associated with the coating parameters (e.g., coating rate) can compensate for imperfections in the coating function (e.g., shadow mask gradient). Conventionally, if a shadow mask is found to provide suboptimal performance, it is replaced. However, the inventors have recognized that by exploiting the degrees of freedom associated with the coating parameters and performing a second (fine-tuning) optimization using the measured coating function, a certain degree of suboptimal performance can be tolerated. This approach results in significant efficiency gains and extends the life of the shadow mask. In other words, the inventors surprisingly discovered that this approach produces uniform and stable coating performance, even after the shadow mask has degraded far from its original specifications throughout its use.

[0064] The method can be further extended to create an iterative loop of re-optimization. In this case, there is also step e: forming or simulating multiple layers using the deviated coating function and adjusted coating parameters of step d. This is followed by step f: determining or simulating the transmittance at multiple locations along the waveguide for multiple different wavelengths. This is followed by step g: repeating steps b through f until the determined / simulated transmittance of step f is within a tolerance of the optimized transmittance of step a. The transmittance of the produced waveguide is measured in step f. This is to allow the loop established in step g of steps b through f to be closed when a waveguide with fully optimized transmittance is produced or simulated. As will be understood by those skilled in the art, this tolerance can be a number of different factors, such as the transmittance at each location being within a set percentage error from the optimized transmittance of step a, or an analysis of a plotted curve of transmittance along the length of the waveguide compared to the curve of optimized transmittance of step a.

[0065] Each coating function can be a percentage change in thickness of a layer along the length of the waveguide from a first end to a second end of the waveguide. The number of permissible coating functions can be between two and six, optionally between two and four, optionally four. Each determined coating function can be linear. The measurement of step c can indicate that the coating function is nonlinear. The layer thickness measurement of step c can be performed by fitting a measured curve of light interacting with the layer to the expected behavior of light at different thicknesses, thereby determining the thickness of the layer. The optical measurement can be performed on light reflected by the layer, or an ellipsometer can be used.

[0066] By having a set number of allowable coating functions, a single application apparatus (a shadow mask as described above) can apply each layer without requiring changes. This increases the efficiency of the system and method.

[0067] The first coating parameter may relate to the thickness of the layer at its thinnest point. Forming the plurality of layers of step b may include using a shadow mask to control the flow of coating material toward the waveguide. The first coating parameter may be one of: a rate of coating material flow toward the waveguide; or a rate at which the waveguide moves through the flow of coating material. Step a may also include determining a third coating parameter, and step d may also include determining a fourth coating parameter, the third and fourth coating parameters being another of: a rate of coating material flow toward the waveguide; or a rate at which the waveguide moves through the flow of coating material. In this case, the fourth coating parameter is a new or updated version of the third coating parameter after the re-optimization (or second optimization) occurs.

[0068] By adjusting the "base thickness" of the waveguide coating, the inventors discovered that the transmittance of each layer can be modified to account for wear in the application equipment, which causes inaccuracies in the coating function of the layer. By using these two parameters, the "base thickness" can be changed without having to change the application equipment.

[0069] The plurality of layers may include at least one dielectric. Forming the plurality of layers in step b may include forming alternating layers of a first material and a second material. The first material may be a first dielectric, and the second material may be a second dielectric, wherein the first dielectric is a first oxide, fluoride, sulfide, or nitrate of a first transition metal or semiconductor, and the second dielectric is a second oxide, fluoride, sulfide, or nitrate of a second transition metal or semiconductor. The difference in refractive index between the first material and the second material may be greater than 0.4.

[0070] As mentioned above, these materials have several advantageous properties for waveguide coatings.

[0071] The plurality of different wavelengths may include a first wavelength, a second wavelength, and a third wavelength. The first wavelength may be in the range of 630-670 nm, the second wavelength may be in the range of 500-540 nm, and the third wavelength may be in the range of 430-470 nm. The optimized transmittance T(n) at each of the plurality of locations along the waveguide may satisfy the following equation: T(n)=(T(n-1)) / ([1-T(n-1)]×[1-L]), where L is the optical loss factor of the waveguide material.

[0072] These follow from the optimal characteristics of the waveguide as described above.

[0073] The optimization of steps a and e may further include taking into account the transmittance of another transmissive coating on the surface opposite to the applied transmissive coating.

[0074] In this way, the applied coating can be tuned to account for inaccuracies in the transmittance of the opposing coated surface. Alternatively or additionally, the applied coating can be tuned to favor or disfavor specific wavelengths of light. This can compensate for the optical properties of the system or create a specific visual effect for the user.

[0075] The deviating coating function can be determined by fitting the original coating function to the measured thickness. This allows the deviating coating function to be accurately identified and quantified for re-optimization in step d.

[0076] The measuring of step c) may include measuring the thickness of each layer. The iterative optimization of step d) may include adjusting the coating parameters of each layer at each of a plurality of locations.

[0077] According to a second aspect, there is provided a transmissive coating for a waveguide applied using the method described above.

[0078] According to a third aspect, there is provided a waveguide comprising a transmissive coating applied using the method described above.The waveguide may further comprise a reflective coating on a surface opposite to the transmissive coating.

[0079] According to a fourth aspect, there is provided a holographic system comprising a display device arranged to display a hologram of an image and output spatially modulated light according to the hologram, and the above-mentioned first waveguide. The holographic system may further comprise a second waveguide.

[0080] According to a fifth aspect, a method for applying a transmissive coating to a waveguide is provided. The transmissive coating comprises a plurality of layers. The method comprises step a: determining first coating parameters and selecting a coating function for each layer to optimize transmittance at a plurality of locations along the waveguide for a plurality of different wavelengths. The coating function is selected from a plurality of permissible coating functions, for example, four permissible coating functions. This is followed by step b: forming the first layer using the determined coating parameters and coating function. This is followed by step c: identifying, by measuring the thickness of at least the first layer at each of the plurality of locations, how the coating function deviates from the coating function determined during the optimization in step a. This is followed by step d: repeating the optimization of the transmittance at a plurality of locations along the waveguide for a plurality of different wavelengths using the measured coating function for each layer, but by adjusting the coating parameters for the second layer. Finally, step e: repeating steps b through d for the second layer and then for each subsequent layer.

[0081] This method is similar to the method of the first aspect, however, in this method, adjustments are made after each layer is formed, accounting for inaccuracies introduced when forming the previous layer. This results in a more optimal coating in a single set of layer applications (i.e., without requiring multiple iterations of suboptimal coatings), but it also results in a less optimal coating than the final version made according to the method of the first aspect. This is at least because viewing the layers holistically allows for better optimization of transmission over the entire length of the waveguide.

[0082] The term "hologram" is used to refer to a record that contains amplitude information or phase information, or some combination thereof, about an object. The term "holographic reconstruction" is used to refer to the optical reconstruction of an object formed by illuminating a hologram. The system disclosed herein is described as a "holographic projector" because the holographic reconstruction is a real image and is spatially separated from the hologram. The term "replay field" is used to refer to the 2D region within which the holographic reconstruction is formed and is perfectly focused. If the hologram is displayed on a spatial light modulator comprising pixels, the replay field will be repeated in the form of multiple diffraction orders, where each diffraction order is a replica of the zeroth order replay field. The zeroth order replay field typically corresponds to the preferred or primary replay field because it is the brightest replay field. Unless otherwise explicitly stated, the term "replay field" should be taken to refer to the zeroth order replay field. The term "replay plane" is used to refer to the plane in space that contains all replay fields. The terms "image," "replay image," and "image area" refer to the area of ​​the replay field that is illuminated by the light of the holographic reconstruction. In some embodiments, an "image" may comprise discrete points, which may be referred to as "image points," or, for convenience only, as "image pixels."

[0083] The terms "encoding," "writing," and "addressing" are used to describe the process of providing a plurality of control values, each of which determines the modulation level of each pixel, to a plurality of pixels of the SLM. It can be said that the pixels of the SLM are configured to "display" a light modulation profile in response to receiving the plurality of control values. Thus, the SLM can be said to "display" a hologram, and a hologram can be considered an array of light modulation values ​​or levels.

[0084] It has been found that holographic reconstructions of acceptable quality can be formed from "holograms" that contain only phase information related to the Fourier transform of the original object. Such holographic recordings may be referred to as phase-only holograms. The embodiments relate to phase-only holograms, but the present disclosure is equally applicable to amplitude-only holography.

[0085] The present disclosure is also applicable to forming a holographic reconstruction using amplitude and phase information associated with the Fourier transform of the original object. In some embodiments, this is achieved by using complex modulation of a so-called full complex hologram that contains amplitude and phase information related to the original object. Because the value (gray level) assigned to each pixel of the hologram has both amplitude and phase components, such a hologram can be referred to as a full complex hologram. The value (gray level) assigned to each pixel can be represented as a complex number having both amplitude and phase components. In some embodiments, a full complex computer-generated hologram is calculated.

[0086] Reference may be made to the phase value, phase component, phase information, or simply phase of a pixel of a computer-generated hologram or spatial light modulator as shorthand for "phase delay". That is, any phase value described is actually a number (e.g., in the range of 0 to 2π) that represents the amount of phase delay provided by that pixel. For example, a pixel of a spatial light modulator described as having a phase value of π / 2 will delay the phase of received light by π / 2 radians. In some embodiments, each pixel of the spatial light modulator can operate at one of a plurality of possible modulation values ​​(e.g., phase delay values). The term "grayscale" may be used to refer to a plurality of available modulation levels. For example, the term "grayscale" may be used for convenience to refer to a plurality of available phase levels in a phase modulator alone, even though the different phase levels do not provide different shades of gray. For convenience, the term "grayscale" may also be used to refer to a plurality of available complex modulation levels in a complex modulator.

[0087] Thus, a hologram comprises an array of gray levels, i.e. an array of light modulation values, such as phase delay values ​​or an array of complex modulation values. A hologram is also considered a diffraction pattern, since it is a pattern that causes diffraction when displayed on a spatial light modulator and illuminated with light of a wavelength relative to (usually less than) the pixel pitch of the spatial light modulator. Reference is made herein to combining a hologram with other diffraction patterns, such as diffraction patterns used as lenses or gratings. For example, a diffraction pattern used as a grating can be combined with a hologram to shift the replay field on the replay plane, or a diffraction pattern used as a lens can be combined with a hologram to focus the holographic reconstruction on the replay plane in the near field.

[0088] Although different embodiments and groups of embodiments may be disclosed separately in the detailed description below, any feature of any embodiment or group of embodiments may be combined with any other feature or combination of features of any embodiment or group of embodiments. That is, all possible combinations and permutations of the features disclosed in this disclosure are contemplated. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Certain embodiments are described, by way of example only, with reference to the following drawings:

[0090] Figure 1 is a schematic diagram showing a reflective SLM producing a holographic reconstruction on a screen;

[0091] Figure 2A A first iteration of an example Gerchberg-Saxton type algorithm is shown;

[0092] Figure 2B The second and subsequent iterations of an example Gerchberg-Saxton type algorithm are shown;

[0093] Figure 2CAn alternative second and subsequent iteration of an example Gerchberg-Saxton type algorithm is shown;

[0094] Figure 3 is a schematic diagram of a reflective LCOS SLM;

[0095] Figure 4A shows an image comprising a plurality of image regions (bottom) and a corresponding hologram comprising a plurality of hologram components (top);

[0096] Figure 4B A hologram is shown characterized by routing or directing holographically encoded light into a plurality of discrete hologram channels;

[0097] Figure 5 shows a system that is arranged to transmit light through different optical paths. Figure 4B The optical content of each hologram channel is delivered to the eye.

[0098] Figure 6 showing a perspective view of a pair of stacked image replicators arranged to expand a light beam in two dimensions;

[0099] Figure 7 shows a schematic cross-sectional view of a first waveguide according to the present disclosure;

[0100] Figure 8 Shown Figure 7 a schematic close-up cross-sectional view of a portion of a first waveguide;

[0101] Figure 9 A graph showing an idealized increased transmittance of a waveguide in the waveguide direction;

[0102] Figure 10A 、 Figure 10B and Figure 10C shows a graph relating to a first example of a waveguide according to the present disclosure comprising 12 alternating layers of SiO2 and TiO2, wherein Figure 10A and 10B The thickness of SiO2 and TiO2 layers are shown respectively, and Figure 10C shows a comparison of the transmittance of the first surface of the waveguide of the first example with the ideal transmittance for the red, green and blue wavelengths for which the waveguide has been designed;

[0103] Figure 11 a graph showing the transmittance of the waveguide of the first example at other wavelengths compared to the ideal transmittance;

[0104] Figure 12 shows a schematic cross-sectional view of a portion of an apparatus for fabricating a waveguide according to the present disclosure, wherein a waveguide substrate passes beneath a source of dielectric material;

[0105] Figure 13 It includes four holes Figure 12 Schematic diagram of the shadow mask of the device, the cross section is located at Figure 12 The plane of the cross section is perpendicular to the plane;

[0106] Figure 14A 、 Figure 14B 、 Figure 14C and Figure 14D Schematic cross-sections of four different waveguide substrates are shown, each with a Figure 13 a shadow mask having layers of dielectric material formed on the first surface, wherein each layer is formed using a different aperture of the shadow mask;

[0107] Figure 15 A first method of applying a transmissive coating to a waveguide according to the present disclosure is shown;

[0108] Figure 16 An extended version of the first method of applying a transmissive coating to a waveguide according to the present disclosure is shown;

[0109] Figure 17 A second method of applying a transmissive coating to a waveguide according to the present disclosure is shown;

[0110] Figure 18A 、 Figure 18B and Figure 18C shows a graph associated with an example of a simulated optimized transmission coating for a waveguide according to the present disclosure, comprising 12 alternating layers of first and second dielectric materials, wherein Figure 18A and 18B The thicknesses of the first and second dielectric material layers are shown, respectively, Figure 18C shows the transmittance of a simulated optimized transmissive coating compared to the ideal transmittance for the red, green, and blue wavelengths for which the transmissive coating has been designed; and

[0111] Figure 19A 、 Figure 19B and Figure 19C shows a graph relating to a first example of a transmissive coating for a waveguide applied according to the method of the present disclosure, comprising 12 alternating layers of first and second dielectric materials, wherein Figure 19A and 19B The thicknesses of the first and second dielectric material layers are shown, respectively, Figure 19C Shown are the transmittances of the transmissive coatings compared to the ideal transmittances for the red, green, and blue wavelengths for which the transmissive coatings have been designed.

[0112] The same reference numbers will be used throughout the drawings to refer to the same or like parts. DETAILED DESCRIPTION

[0113] The present invention is not limited to the embodiments described below, but extends to the full scope of the appended claims. That is, the present invention can be embodied in different forms and should not be construed as limited to the described embodiments, which are set forth for illustrative purposes.

[0114] Unless otherwise stated, terms in the singular may include plural forms.

[0115] A structure described as being formed on / under or above / below another structure should be construed to include a case where the structures are in contact with each other and, further, a case where a third structure is provided therebetween.

[0116] When describing a temporal relationship, for example, when the temporal order of events is described as "after," "followed," "next," "before," etc., the present disclosure should be considered to include both consecutive and non-consecutive events unless otherwise specified. For example, unless terms such as "just," "immediately," or "directly" are used, the description should be considered to include non-consecutive situations.

[0117] Although the terms "first," "second," etc. may be used herein to describe various elements, these elements are not limited by these terms. These terms are only used to distinguish between the various elements. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element without departing from the scope of the appended claims.

[0118] The features of different embodiments may be coupled or combined with each other in part or in whole, and may interoperate with each other in different ways. Some embodiments may be performed independently of each other, or may be performed together in a mutually dependent relationship.

[0119] Optical configuration

[0120] Figure 1 An embodiment is shown in which a computer-generated hologram is encoded on a single spatial light modulator. The computer-generated hologram is a Fourier transform of the object being reconstructed. Thus, the hologram can be said to be a Fourier, frequency, or spectral domain representation of the object. In this embodiment, the spatial light modulator is a reflective liquid crystal on silicon (LCOS) device. The hologram is encoded on the spatial light modulator, and a holographic reconstruction is formed at a replay field, such as a light-receiving surface like a screen or diffuser.

[0121] A light source 110, such as a laser or laser diode, is arranged to illuminate the SLM 140 via a collimating lens 111. The collimating lens causes a substantially planar wavefront of light to be incident on the SLM. Figure 1In embodiments, the direction of the wavefront is off-normal (e.g., two or three degrees from a plane that is truly normal to the transparent layer). However, in other embodiments, a substantially planar wavefront is provided at normal incidence, and a beam splitter arrangement is used to separate the input and output optical paths. Figure 1 In the embodiment shown, the arrangement is such that light from the light source reflects from the mirrored back surface of the SLM and interacts with the light modulating layer to form an exit wavefront 112. The exit wavefront 112 is applied to an optical device including a Fourier transform lens 120, the focus of which is located at a screen 125. More specifically, the Fourier transform lens 120 receives the modulated light beam from the SLM 140 and performs a frequency-to-space transform to produce a holographic reconstruction at the screen 125.

[0122] It's important to note that in this type of hologram, every pixel of the hologram contributes to the entire reconstruction. There is no one-to-one correlation between a specific point on the replay field (or image pixel) and a specific light modulation element (or hologram pixel). In other words, the modulated light leaving the light modulation layer is distributed across the entire replay field.

[0123] In these embodiments, the position of the holographic reconstruction in space is determined by the power (focus) of the Fourier transform lens. Figure 1 In the illustrated embodiment, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens and optically performs a Fourier transform. Any lens can function as a Fourier transform lens, but the accuracy of the Fourier transform it performs will be limited by the lens's performance. Those skilled in the art understand how to use lenses to perform an optical Fourier transform.

[0124] Hologram computing

[0125] In some embodiments, the computer-generated hologram is a Fourier transform hologram, or simply a Fourier hologram or a Fourier-based hologram, in which the image is reconstructed in the far field by utilizing the Fourier transform properties of a positive lens. The Fourier hologram is calculated by Fourier transforming the desired light field in the replay plane back to the lens plane. The computer-generated Fourier hologram can be calculated using the Fourier transform.

[0126] Algorithms such as the Gerchberg-Saxton algorithm can be used to calculate Fourier transform holograms. Furthermore, the Gerchberg-Saxton algorithm can be used to calculate a hologram in the Fourier domain (i.e., a Fourier transform hologram) from amplitude-only information in the spatial domain (e.g., a photograph). Phase information about the object is effectively "retrieved" from amplitude-only information in the spatial domain. In some embodiments, computer-generated holograms are calculated from amplitude-only information using the Gerchberg-Saxton algorithm or a variation thereof.

[0127] The Gerchberg-Saxton algorithm considers that when the intensity cross section I of the beam in planes A and B is known, A (x,y) and I B (x,y) and I A (x,y) and I B (x,y) is related by a single Fourier transform. For a given intensity cross section, the phase distribution approximation Ψ in planes A and B is obtained separately A (x,y) and Ψ B (x,y). The Gerchberg-Saxton algorithm finds the solution to this problem by following an iterative process. More specifically, the Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeatedly transferring representations of I between the spatial domain and the Fourier (spectral or frequency) domain. A (x,y) and I B A data set (amplitude and phase) of (x, y) is obtained. A corresponding computer-generated hologram in the spectral domain is obtained by at least one iteration of the algorithm. The algorithm is convergent and is arranged to produce a hologram representing the input image. The hologram can be an amplitude-only hologram, a phase-only hologram, or a full complex hologram.

[0128] In some embodiments, a phase-only hologram is calculated using an algorithm based on the Gerchberg-Saxton algorithm, such as the algorithm described in UK Patent 2498170 or 2501112, the entire contents of which are incorporated herein by reference. However, the embodiments disclosed herein describe calculating a phase-only hologram by way of example only. In these embodiments, the Gerchberg-Saxton algorithm retrieves the phase information Ψ[u,v] of the Fourier transform of a data set, which produces known amplitude information T[x,y], where the amplitude information T[x,y] represents a target image (e.g., a photograph). Since amplitude and phase are inherently combined in the Fourier transform, the transformed amplitude and phase contain useful information about the accuracy of the calculated data set. Therefore, the algorithm can be used iteratively with feedback of the amplitude and phase information. However, in these embodiments, only the phase information Ψ[u,v] is used as a hologram to form a holographic representation of the target image at the image plane. A hologram is a data set (e.g., a 2D array) of phase values.

[0129] In other embodiments, an algorithm based on the Gerchberg-Saxton algorithm is used to calculate a full complex hologram. A full complex hologram is a hologram having an amplitude component and a phase component. A hologram is a data set (e.g., a 2D array) comprising an array of complex data values, where each complex data value comprises an amplitude component and a phase component.

[0130] In some embodiments, the algorithm processes complex data and the Fourier transform is a complex Fourier transform. The complex data can be viewed as comprising (i) a real component and an imaginary component, or (ii) an amplitude component and a phase component. In some embodiments, the two components of the complex data are processed differently at various stages of the algorithm.

[0131] Figure 2A A first iteration of an algorithm for calculating a phase-only hologram according to some embodiments is shown. The input to the algorithm is an input image 210 comprising a 2D array of pixels or data values, wherein each pixel or data value is an amplitude or magnitude value. That is, each pixel or data value of the input image 210 does not have a phase component. Therefore, the input image 210 can be regarded as an amplitude-only or amplitude-only or intensity-only distribution. An example of such an input image 210 is a frame of a photograph or a video comprising a time sequence of frames. The first iteration of the algorithm begins with a data formation step 202A, which comprises assigning a random phase value to each pixel of the input image using a random phase distribution (or random phase seed) 230 to form a starting complex data set, wherein each data element of the data set comprises an amplitude and a phase. It can be said that the starting complex data set represents the input image in the spatial domain.

[0132] First processing block 250 receives an initial complex data set and performs a complex Fourier transform to form a Fourier-transformed complex data set. Second processing block 253 receives the Fourier-transformed complex data set and outputs hologram 280A. In some embodiments, hologram 280A is a phase-only hologram. In these embodiments, second processing block 253 quantizes each phase value and sets each amplitude value to 1 to form hologram 280A. Each phase value is quantized according to a phase level that can be represented at a pixel of a spatial light modulator that will be used to "display" the phase-only hologram. For example, if each pixel of the spatial light modulator provides 256 different phase levels, each phase value of the hologram is quantized to one of the 256 possible phase levels. Hologram 280A is a phase-only Fourier hologram representing the input image. In other embodiments, hologram 280A is a full complex hologram, comprising an array of complex data values ​​(each including an amplitude component and a phase component) derived from the received Fourier-transformed complex data set. In some embodiments, second processing block 253 constrains each complex data value to one of a plurality of permissible complex modulation levels to form hologram 280A. The constraining step may include setting each complex data value to the closest permissible complex modulation level in the complex plane. Hologram 280A can be said to represent the input image in the spectral, Fourier, or frequency domain. In some embodiments, the algorithm stops at this point.

[0133] However, in other embodiments, the algorithm continues as Figure 2AIn other words, following Figure 2A The steps indicated by dashed arrows are optional (ie, not essential for all embodiments).

[0134] The third processing block 256 receives the modified complex data set from the second processing block 253 and performs an inverse Fourier transform to form an inverse Fourier transformed complex data set. The inverse Fourier transformed complex data set can be said to represent the input image in the spatial domain.

[0135] Fourth processing block 259 receives the inverse Fourier transformed complex data set and extracts the distribution of amplitude values ​​211A and the distribution of phase values ​​213A. Optionally, fourth processing block 259 evaluates the distribution of amplitude values ​​211A. Specifically, fourth processing block 259 may compare the distribution of amplitude values ​​211A of the inverse Fourier transformed complex data set with input image 510, which itself is a distribution of amplitude values. If the difference between the distribution of amplitude values ​​211A and input image 210 is sufficiently small, fourth processing block 259 may determine that hologram 280A is acceptable. In other words, if the difference between the distribution of amplitude values ​​211A and input image 210 is sufficiently small, fourth processing block 259 may determine that hologram 280A is a sufficiently accurate representation of input image 210. In some embodiments, the distribution of phase values ​​213A of the inverse Fourier transformed complex data set is ignored for comparison purposes. It will be appreciated that any number of different methods may be employed to compare the distribution of amplitude values ​​211A to the input image 210, and the present disclosure is not limited to any particular method. In some embodiments, a mean square error is calculated, and if the mean square error is less than a threshold, the hologram 280A is deemed acceptable. If the fourth processing block 259 determines that the hologram 280A is unacceptable, further iterations of the algorithm may be performed. However, this comparison step is not required, and in other embodiments, the number of iterations of the algorithm performed is predetermined, preset, or user-defined.

[0136] Figure 2B 2 represents the second iteration of the algorithm and any further iterations of the algorithm. The distribution of phase values ​​213A from the previous iteration is fed back through the processing blocks of the algorithm. The distribution of amplitude values ​​211A is rejected in favor of the distribution of amplitude values ​​of the input image 210. In the first iteration, the data forming step 202A forms a first complex data set by combining the distribution of amplitude values ​​of the input image 210 with the random phase distribution 230. However, in the second and subsequent iterations, the data forming step 202B includes forming a complex data set by combining (i) the distribution of phase values ​​213A from the previous iteration of the algorithm with (ii) the distribution of amplitude values ​​of the input image 210.

[0137] Then, with reference to Figure 2AThe same method as described is handled by Figure 2B The complex data set formed in step 202B is used to form the second iterative hologram 280B. Therefore, the description of the process is not repeated here. When the second iterative hologram 280B has been calculated, the algorithm can stop. However, any number of further iterations of the algorithm can be performed. It will be understood that the third processing block 256 is only required when the fourth processing block 259 is required or further iterations are required. The output hologram 280B generally gets better with each iteration. However, in practice, a point is often reached where no measurable improvement can be observed, or the positive benefits of performing further iterations are offset by the negative effects of the additional processing time. Therefore, the algorithm is described as iterative and convergent.

[0138] Figure 2C 213A for the previous iteration is fed back through a processing block of the algorithm. The distribution of amplitude values ​​211A is rejected in favor of an alternative distribution of amplitude values. In this alternative embodiment, the alternative distribution of amplitude values ​​is derived from the distribution of amplitude values ​​211 for the previous iteration. Specifically, processing block 258 subtracts the distribution of amplitude values ​​of input image 210 from the distribution of amplitude values ​​211 for the previous iteration, scales the difference by a gain factor α, and subtracts the scaled difference from input image 210. This is mathematically expressed by the following equation, where the subscript text and number represent the number of iterations:

[0139] R n+1 [x,y]=F'{exp(iψ n [u,v])}

[0140] ψ n [u,v]=DF{η·exp(i∠R n [x,y])}

[0141] η=T[x,y]-α(R n [x,y]|-T[x,y])

[0142] in:

[0143] F' is the inverse Fourier transform;

[0144] F is the forward Fourier transform;

[0145] R[x,y] is the complex data set output by the third processing block 256;

[0146] T[x,y] is the input or target image;

[0147] ∠ is the phase component;

[0148] Ψ is the phase-only hologram 280B;

[0149] η is the new distribution of amplitude values ​​211B; and

[0150] α is the gain factor.

[0151] The gain factor α may be fixed or variable. In some embodiments, the gain factor α is determined based on the size and rate of the input target image data. In some embodiments, the gain factor α depends on the number of iterations. In some embodiments, the gain factor α is only a function of the number of iterations.

[0152] In all other respects, Figure 2C Examples and Figure 2A and Figure 2B It can be said that only the phase hologram Ψ(u,v) comprises the phase distribution in the frequency or Fourier domain.

[0153] In some embodiments, a spatial light modulator is used to perform a Fourier transform. Specifically, the hologram data is combined with a second data that provides optical power. That is, the data written to the spatial light modulation includes hologram data representing the object and lens data representing the lens. When displayed on the spatial light modulator and illuminated with light, the lens data simulates a physical lens - that is, it focuses light in the same way as a corresponding physical optical element. Therefore, the lens data provides optical power or focusing power. In these embodiments, the optical power can be omitted. Figure 1A physical Fourier transform lens 120 is shown. It is known how to calculate data representing a lens. This data representing a lens can be referred to as a software lens. For example, a phase-only lens can be formed by calculating the phase delay caused by each point of the lens due to its refractive index and spatially varying optical path length. For example, the optical path length at the center of a convex lens is greater than the optical path length at the edge of the lens. An amplitude-only lens can be formed using a Fresnel zone plate. In the field of computer-generated holography, it is also known how to combine data representing a lens with a hologram, thereby performing a Fourier transform of the hologram without requiring a physical Fourier lens. In some embodiments, the lensing data is combined with the hologram via a simple addition, such as simple vector addition. In some embodiments, a physical lens is used in conjunction with a software lens to perform the Fourier transform. Alternatively, in other embodiments, the Fourier transform lens is omitted entirely, allowing holographic reconstruction to occur in the far field. In further embodiments, the hologram can be combined in the same manner with grating data—data arranged to perform a grating function, such as image steering. Again, it is known in the art how to calculate such data. For example, a phase-only grating can be formed by modeling the phase delay caused by each point on the surface of the blazed grating. An amplitude-only grating can simply be superimposed with an amplitude-only hologram to provide angular steering for the holographic reconstruction. The second data providing lensing and / or steering can be referred to as a light processing function or light processing pattern to distinguish it from the hologram data, which can be referred to as an image forming function or image forming pattern.

[0154] In some embodiments, the Fourier transform is performed jointly by a physical Fourier transform lens and a software lens. That is, some of the optical power contributing to the Fourier transform is provided by the software lens, while the remaining optical power contributing to the Fourier transform is provided by one or more physical optical devices.

[0155] In some embodiments, a real-time engine is provided that uses an algorithm to receive image data and calculate holograms in real time. In some embodiments, the image data is a video comprising a sequence of image frames. In other embodiments, the holograms are pre-calculated, stored in computer memory, and recalled as needed for display on the SLM. That is, in some embodiments, a repository of pre-determined holograms is provided.

[0156] The embodiments relate to Fourier holography and Gerchberg-Saxton type algorithms by way of example only. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms that can be calculated using similar methods. The present disclosure is also applicable to holograms calculated using other techniques, such as point cloud-based techniques.

[0157] Optical Modulation

[0158] A spatial light modulator can be used to display diffraction patterns, including computer-generated holograms. If the hologram is a phase-only hologram, a spatial light modulator that modulates the phase is required. If the hologram is a fully complex hologram, a spatial light modulator that modulates both phase and amplitude can be used, or a first spatial light modulator that modulates the phase and a second spatial light modulator that modulates the amplitude can be used.

[0159] In some embodiments, the light modulation elements (i.e., pixels) of the spatial light modulator are cells comprising liquid crystals. That is, in some embodiments, the spatial light modulator is a liquid crystal device in which the optically active component is a liquid crystal. Each liquid crystal cell is configured to selectively provide multiple light modulation levels. That is, each liquid crystal cell is configured to operate at a light modulation level selected from a plurality of possible light modulation levels at any time. Each liquid crystal cell can be dynamically reconfigured to a light modulation level that is different from the plurality of light modulation levels. In some embodiments, the spatial light modulator is a reflective liquid crystal on silicon (LCOS) spatial light modulator, but the present disclosure is not limited to this type of spatial light modulator.

[0160] LCOS devices provide a dense array of light modulating elements or pixels within a small aperture (e.g., a few centimeters wide). The pixels are typically around 10 microns or smaller, which results in a diffraction angle of a few degrees, meaning the optical system can be compact. It is much easier to fully illuminate the small aperture of an LCOS SLM than the large apertures of other liquid crystal devices. LCOS devices are typically reflective, which means that the circuitry that drives the LCOS SLM pixels can be buried under the reflective surface. This results in a higher aperture ratio. In other words, the pixels are densely packed, meaning there is almost no dead space between pixels. This is advantageous because it reduces optical noise in the playback field. LCOS SLMs use a silicon backplane, which has the advantage that the pixels are optically flat. This is particularly important for phase modulation devices.

[0161] The following is just an example, Figure 3 A suitable LCOS SLM is described below. An LCOS device is formed using a single crystal silicon substrate 302. It has a 2D array of square planar aluminum electrodes 301, separated by gaps 301A, arranged on the upper surface of the substrate. Each electrode 301 can be addressed by circuitry 302A buried in the substrate 302. Each electrode forms its own plane mirror. An orientation layer 303 is disposed on the electrode array, and a liquid crystal layer 304 is disposed on the orientation layer 303. A second orientation layer 305 is disposed on a planar transparent layer 306, for example, made of glass. A single transparent electrode 307, for example, made of ITO, is disposed between the transparent layer 306 and the second orientation layer 305.

[0162] Each square electrode 301, together with the footprint of the transparent electrode 307 and the intervening liquid crystal material, defines a controllable phase-modulating element 308, commonly referred to as a pixel. The effective pixel area, or fill factor, is the percentage of the total pixel that is optically active, taking into account the spaces between pixels 301A. By controlling the voltage applied to each electrode 301 relative to the transparent electrode 307, the properties of the liquid crystal material of each phase-modulating element can be varied, thereby providing variable retardation to light incident thereon. The effect is to provide only phase modulation of the wavefront, i.e., no amplitude effects occur.

[0163] The described LCOS SLM outputs spatially modulated light in a reflective manner. A reflective LCOS SLM has the advantage that the signal lines, grating lines and transistors are located below the mirror surface, which results in a high fill factor (typically greater than 90%) and high resolution. Another advantage of using a reflective LCOS spatial light modulator is that the thickness of the liquid crystal layer can be half that required when using a transmissive device. This greatly increases the switching speed of the liquid crystal (a key advantage for projecting moving video images). However, the teachings of the present disclosure can also be implemented using a transmissive LCOS SLM.

[0164] Optical Channel

[0165] The optical systems disclosed herein are applicable to pupil expansion with any diffracted light field. In some embodiments, the diffracted light field is a holographic light field—that is, a composite light field that is spatially modulated according to a hologram of an image rather than the image itself. In some embodiments, the hologram is a special type of hologram that angularly divides / directs the image content. This type of hologram is further described herein merely as an example of a diffracted light field compatible with the present disclosure. Other types of holograms can be used in conjunction with the display systems and light engines disclosed herein.

[0166] Display systems and methods are described below that include a waveguide pupil expander. As will be familiar to the skilled reader, a waveguide may be considered a "pupil expander" because it can be used to increase the area over which light emitted by a relatively small light emitter (e.g., a relatively small SLM or other pixelated display device used in the apparatus described herein) can be viewed by a human observer or other viewing system located at a distance (e.g., a relatively large distance) away from the light emitter. The waveguide achieves this by increasing the number of transmission points through which light is output toward the observer. As a result, light can be seen from multiple different observer positions, e.g., an observer may be able to move their head, and thereby their line of sight, while still being able to see light from the light emitter. Thus, it can be said that by using a waveguide pupil expander, the observer's "eye box" or "eye motion box" is enlarged. This has many useful applications, such as, but not limited to, heads-up displays, such as, but not limited to, automotive heads-up displays.

[0167] The display systems described herein can be configured to direct light, such as a diffracted light field, through a waveguide pupil expander so as to provide pupil expansion in at least one dimension, such as in two dimensions. The diffracted light field may include light output by a spatial light modulator (SLM), such as an LCOS SLM. For example, the diffracted light field may include light encoded by a hologram displayed by the SLM. For example, the diffracted light field may include light of a holographically reconstructed image, corresponding to the hologram displayed by the SLM. The hologram may include a computer generated hologram (CGH), such as, but not limited to, a point cloud hologram, a Fresnel hologram, or a Fourier hologram. The hologram may be referred to as a "diffraction structure" or a "modulation pattern". The SLM or other display device may be arranged to display a diffraction pattern (or modulation pattern) in a manner familiar to the skilled reader, comprising a hologram and one or more other elements, such as a soft lens or a diffraction grating.

[0168] The hologram can be calculated to provide channels of the diffracted light field. This is described in detail in GB2101666.2, GB2101667.0 and GB2112213.0, all of which are incorporated herein by reference. In general, the hologram can be calculated to correspond to the image to be holographically reproduced. The image to which the hologram corresponds can be referred to as the "input image" or "target image". The hologram can be calculated so that when it is displayed on the SLM and appropriately illuminated, it forms a light field (output by the SLM) comprising a spatially modulated light cone. In some embodiments, the cone comprises a plurality of continuous light channels of spatially modulated light, which correspond to corresponding continuous regions of the image. However, the present disclosure is not limited to this type of hologram.

[0169] Although referred to herein as "holograms" or "computer generated holograms (CGHs)", it should be understood that the SLM can be configured to dynamically display multiple different holograms continuously or according to a sequence. The systems and methods described herein are suitable for dynamic display of multiple different holograms.

[0170] Figures 4A to 5 An example of the type of hologram that can be displayed on a display device, such as an SLM, that can be used in conjunction with the pupil expander disclosed herein is shown. However, this example should not be viewed as limiting the present disclosure.

[0171] Figure 4A An image 452 is shown for projection, comprising eight image regions / components V1 to V8. By way of example only, Figure 4A Eight image components are shown, and image 452 may be separated into any number of components. Figure 4AAlso shown is a coded light pattern 454 (i.e., a hologram) that can reconstruct image 452, for example, when transformed by a lens of a suitable viewing system. The coded light pattern 454 includes first through eighth sub-holograms or components H1 through H8, corresponding to first through eighth image components / regions V1 through V8. Figure 4A It further shows how a hologram decomposes the image content by angle. Therefore, a hologram is characterized by its guidance of light. Figure 4B Specifically, the hologram in this example directs light into multiple discrete regions. In the example shown, the discrete regions are disks, but other shapes are also contemplated. After propagation through the waveguide, the optimal disk size and shape can be correlated to the size and shape of the entrance pupil of the optical observation system.

[0172] Figure 5 An observation system 500 is shown, including a display such as Figure 4A and 4B A display device for a computed hologram is shown.

[0173] Observation system 500 includes a display device that, in this arrangement, includes an LCOS 502. LCOS 502 is arranged to display a modulation pattern (or "diffraction pattern") comprising a hologram and projects holographically encoded light into an eye 505, which includes a pupil serving as an aperture 504, a lens 509, and a retina (not shown) serving as an observation plane. There is a light source (not shown) arranged to illuminate LCOS 502. The lens 509 of eye 505 performs the conversion of the hologram into an image. The light source can be of any suitable type. For example, it can include a laser source.

[0174] The viewing system 500 also includes a waveguide 508 located between the LCOS 502 and the eye 505. The presence of the waveguide 508 enables all angular content from the LCOS 502 to be received by the eye, even at the relatively large projection distance shown. This is because the waveguide 508 acts as a pupil expander in a well-known manner and will therefore only be briefly described here.

[0175] in short, Figure 5Waveguide 508 is shown comprising a generally elongated structure. In this example, waveguide 508 comprises an optical plate of refractive material, but other types of waveguides are well known and may be used. Waveguide 508 is positioned to intersect the light cone (i.e., the diffracted light field) projected from LCOS 502, for example, at an oblique angle. In this example, the size, position, and orientation of waveguide 508 are configured to ensure that light from each of the eight light beams within the light cone enters waveguide 508. Light from the light cone enters waveguide 508 via a first planar surface of waveguide 508 (located closest to LCOS 502) and is guided at least partially along the length of waveguide 508 before being emitted via a second planar surface of waveguide 508, substantially opposite the first surface (located closest to the eye). As will be readily appreciated, the second planar surface is partially reflective and partially transmissive. In other words, as each light ray propagates within waveguide 508 from the first planar surface and strikes the second planar surface, some light will be transmitted through waveguide 508, and some light will be reflected by the second planar surface back toward the first planar surface. The first planar surface is reflective so that all light striking it from within the waveguide 508 will be reflected back toward the second planar surface. Thus, some light may simply be refracted between the two planar surfaces of the waveguide 508 before being transmitted, while other light may be reflected and, therefore, may experience one or more reflections (or "bounces") between the planar surfaces of the waveguide 508 before being transmitted.

[0176] Figure 5 A total of nine "bounce" points B0 to B8 are shown along the length of waveguide 508. Figure 4A As shown, light associated with all points of the image (V1-V8) is transmitted out of the waveguide at each "bounce" from the second planar surface of the waveguide 508, but only light from one angular portion of the image (e.g., light from one of V1 to V8) has a trajectory that enables it to reach the eye 505 from each corresponding "bounce" point B0 to B8. In addition, light from a different angular portion of the image (V1 to V8) reaches the eye 505 from each corresponding "bounce" point. Therefore, Figure 5 In the example shown, each angular channel of coded light reaches the eye only once from waveguide 508.

[0177] The above methods and apparatus can be implemented in a variety of different applications and viewing systems. For example, they can be implemented in a head-up display (HUD) or in a head or helmet mounted device (HMD) such as an augmented reality (AR) HMD.

[0178] Although virtual images have been discussed generally herein, which require the eye to convert received modulated light to form a perceived image, the methods and apparatus described herein can be applied to real images.

[0179] 2D pupil expansion

[0180] Although Figure 5 The arrangement shown includes a single waveguide that provides pupil expansion in one dimension, but pupil expansion can be provided in more than one dimension, for example in two dimensions. Figure 5 The examples in use a hologram that has been calculated to create channels of light, each corresponding to a different portion of an image, but the present disclosure and the systems described below are not limited to this type of hologram.

[0181] Figure 6 A perspective view of a system 600 is shown, comprising two replicators 604, 606 arranged to expand a light beam 602 in two dimensions.

[0182] exist Figure 6 In the system 600, the first replicator 604 includes a first pair of surfaces stacked parallel to each other, arranged in a manner similar to Figure 5 The first pair of surfaces are similar in size and shape to each other (in some cases identical) and are substantially elongated in one direction. The collimated light beam 602 is directed to the input of the first replicator 604. Due to internal reflection processes between the two surfaces, as well as from one of the surfaces (the upper surface, such as Figure 6 As will be familiar to the skilled reader, light from beam 602 is replicated in a first direction along the length of first replicator 604, by partially transmitting light from each of a plurality of output points on a first replicator 604. Thus, a first plurality of replica light beams 608 are emitted from first replicator 604 toward second replicator 606.

[0183] The second replicator 606 includes a second pair of surfaces stacked parallel to one another, arranged to receive each collimated beam of the first plurality of light beams 608, and further arranged to provide replication or pupil expansion by expanding each of these beams in a second direction that is substantially orthogonal to the first direction. The first pair of surfaces are similar in size and shape to one another (in some cases identical), and are substantially rectangular. The rectangular shape is implemented for the second replicator so that it has a length along the first direction to receive the first plurality of light beams 608, and a length along the second orthogonal direction to provide replication in the second direction. Due to internal reflection processes between the two surfaces, as well as from one of the surfaces (such as Figure 6 The light of each beam in the first plurality of light beams 608 is replicated in the second direction by partial transmission of light from each of the plurality of output points on the upper surface (as shown in FIG. 1 ). Thus, a second plurality of light beams 610 is emitted from the second replicator 606, wherein the second plurality of light beams 610 includes a replica of the input light beam 602 along each of the first and second directions. Thus, the second plurality of light beams 610 can be viewed as a two-dimensional grid or array including replicated light beams.

[0184] Therefore, it can be said that Figure 6 The first and second replicators 604, 605 are combined to provide a two-dimensional replicator (or "two-dimensional pupil expander").

[0185] Improved waveguide

[0186] As about Figure 5 As described above, the light in the waveguide 508 is reflected between the partially reflective, partially transmissive surfaces and the reflective surface of the waveguide. The light can undergo one or more reflections or bounces between the two reflective / reflective-transmissive plane surfaces, and at each bounce point on the partially transmissive surface, the light is split so that a portion of the light is emitted out of the waveguide, while the remaining (usually larger) portion of the light is reflected to continue propagating between the two surfaces of the waveguide. This effectively results in the partially transmissive surface of the waveguide providing multiple (n) light emission zones for the light waveguided between the first surface and the second surface. After each bounce point / emission zone, the intensity of the light propagating in the waveguide will decrease. In other words, the intensity of the light propagating in the waveguide decreases in the direction of the waveguide.

[0187] Ideally, the intensity of light emitted from the waveguide at each of the n light emitting regions is substantially the same. This can be achieved by providing an improved waveguide in which a layered coating is provided on a partially transmissive surface of the waveguide such that the transmittance of the partially transmissive surface decreases in the direction of the waveguide. This results in a reduction in the intensity of the propagating light in the direction of the waveguide.

[0188] Figure 7 FIG is a schematic cross-sectional view of a waveguide 708 according to the present disclosure. The waveguide 708 includes a first surface 702 and a second surface 704. The light field 706 (at Figure 7 7. A light field (represented by a ray in FIG. 7 ) is shown propagating through waveguide 708. Second surface 704 includes an input port arranged to receive the light field. First surface 702 is partially transmissive, partially reflective, and includes coating 703. The term "coating" is used herein merely for convenience, and one skilled in the art will understand that a component described as a "coating" may be formed by any method, including, but not limited to, a coating process. Second surface 704 is substantially fully reflective (except at the input). Figure 7 The path of a light field through the waveguide is shown, bouncing between the first and second surfaces. At each reflection at the first surface, the light field is split, so that a portion of the light field is emitted through the first surface, while the remainder is reflected and continues to propagate between the first and second surfaces by reflection. Thus, an emission zone is effectively formed at each reflection point. Figure 7 Six emissive regions are shown, however those skilled in the art will appreciate that there may of course be a greater or lesser number of reflective and emissive regions. Figure 7 Just illustrative.

[0189] The coating 703 includes a plurality of layers of a first dielectric and a plurality of layers of a second dielectric arranged alternately. Figure 8 . The layers of the coating are numbered herein, with the layer in contact with the first surface 702 being the first layer (layer 901). Layer 902 is on top of layer 901, and layer 903 is on top of layer 902. The layer on top of layer 903, the layer furthest from the first surface 702, is the fourth layer 904. In this example, layers 901 and 903 are formed of silicon dioxide (SiO2), and layers 902 and 904 are formed of titanium dioxide (TiO2), such that the layers are in an alternating configuration, with subsequent layers of SiO2 (the first dielectric) separated by layers of TiO2 (the second dielectric).

[0190] Each of the layers 901 to 904 is in the waveguide direction ( Figure 9 906) has a varying thickness and, in this embodiment, by way of example, a linear profile. In other words, the rate of change in thickness of each layer is constant. The profile of each layer can be characterized by a percent change in thickness. Each layer has a first end 906 and a second end 908. The percent change in thickness is defined as the change in thickness from the first end 906 to the second end 908 divided by the thickness at the first end 906 multiplied by 100. For the first layer 901, the percent change in thickness is 100 x (final thickness 912 - initial thickness 910) / initial thickness 910.

[0191] Layer 903 has the same percentage change in thickness as layer 901. Furthermore, the percentage change values ​​for layers 901 and 903 are both positive (i.e., the thickness of the layer increases from first end 906 to second end 908). Layers 902 and 904 have different percentage changes from each other and from layers 901 and 903. Furthermore, the percentage changes for layers 902 and 904 are both negative (i.e., the thickness of the layer decreases from first end 906 to second end 908).

[0192] The inventors have discovered that by selecting an appropriate number of alternating layers of first and second dielectrics, with appropriate thicknesses and thickness percentage variations from the first end to the second end, it is possible to provide a first surface of a waveguide having increasing transmittance in the waveguide direction. This allows the intensity of the light field emitted in each emission region (i.e., the intensity of each replica emitted in each emission region) to be substantially constant. This advantageously allows for substantially spatially uniform light emission from the waveguide.

[0193] Figure 9 The ideal exponential growth of the transmittance of the first surface 702 is shown in FIG. 1 , which is a graph showing transmittance on the Y-axis and position along the first surface 702 on the X-axis. The numbers on the X-axis represent n emission regions. Specifically, the transmittance increases according to the following equation: where L is the optical loss factor of the waveguide material.

[0194] Figure 8 The examples shown are representative only. Figure 8 Not drawn to scale. Typically, coatings according to the present invention include more than four layers. Nine examples of layered coatings according to the present disclosure are disclosed below that provide a satisfactory increase in transmittance of the first surface. Each of these examples was determined by simulation. Those skilled in the art will appreciate that the present disclosure is not limited to the examples disclosed herein. For example, the coating can include a different number of layers (more or fewer) than the coatings disclosed herein. In addition, layers of different dielectric materials can be used.

[0195] Example waveguide

[0196] Figures 10A to 10C A first real example of a coating according to the invention disclosed herein is provided. The coating of this first example comprises 12 alternating layers of SiO2 and TiO2. The layers are numbered 1 to 12 such that light emitted from the waveguide passes through each of layers 1 to 12 in sequence. The odd-numbered layers (layers L1, L3, L5, L7, L9, and L11) are SiO2 layers. The even-numbered layers (layers L2, L4, L6, L8, L10, and L12) are TiO2 layers.

[0197] Figure 10A and 10B The figure shows how the thickness of each layer varies with distance along the first surface of the waveguide (i.e., from the first end to the second end of each layer). The Y-axis represents thickness and the X-axis represents position along the waveguide. The numbers 1 to 10 on the X-axis represent the emitting area of ​​the first surface. Figure 10A The SiO2 layers (ie the odd-numbered layers in this example) are shown. Figure 10b shows the TiO2 layers (ie the even-numbered layers in this example).

[0198] like Figure 10A As shown, there are two subsets of SiO2 layers. The first subset of layers has a first value of the percentage change in thickness. These layers are composed of Figure 10A The second subset of layers has a second value of the thickness percentage change that is different from the first subset. These layers are Figure 10A The first and second values ​​in this example are both negative. In this example, the first value of the percentage change is -50% + / - 10%. The second value of the percentage change is -60% + / - 10%. For the avoidance of doubt, the first value is different from the second value. The minimum thickness of the thinnest layer is 50nm + / - 15nm.

[0199] like Figure 10B As shown, there are two subsets of TiO2 layers. The first subset of layers has a third value of thickness percentage variation. These layers are composed of Figure 10BThe second subset of layers has a fourth value of thickness percentage variation that is different from the first subset. These layers are represented by Figure 10B The dashed line in FIG. 1 is shown. The first and second values ​​in this example are both positive. In this example, the third value of the percentage change is 20% + / - 10%. The fourth value of the percentage change is 60% + / - 10%. The minimum thickness of the thinnest layer is 50 nm + / - 15 nm.

[0200] Those skilled in the art will appreciate that while the percentage change in thickness of two layers may be the same, the maximum and minimum thicknesses of these layers may be different. For example, a first layer having a minimum thickness of 2 nm and a maximum thickness of 4 nm has a percentage increase of 100%. A second layer having a minimum thickness of 5 nm and a maximum thickness of 10 nm also has a percentage increase of 100%, even though the absolute thicknesses of the two layers are different.

[0201] Coated waveguides according to the present disclosure typically behave differently at different wavelengths. As will be appreciated by those skilled in the art, a combination of blue, green, and red light sources can be used to provide a full-color image (i.e., light having three different wavelengths). For example, in many holographic systems, blue, green, and red light sources are used to produce a full-color image. If the waveguides of the present disclosure are suitable for use in such systems, then the transmittance of the coated first surface at each desired wavelength should substantially follow Figure 9 Ideal transmittance shown.

[0202] Figure 10C Graph showing transmittance of the first surface of the waveguide of the first example. The Y-axis represents transmittance. The X-axis represents the nth emission region along the first surface of the waveguide. Figure 10C The solid line (unbroken line) 1002 represents the ideal transmission behavior (also Figure 9 The three dashed (interrupted) lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. Figure 10C The three wavelengths shown relate to blue laser light 1004, green laser light 1006, and red laser light 1008, respectively. Figure 10C It is shown how the coating of the first example provides good transmission properties at each of the three wavelengths.

[0203] The inventors have realized that when the problem of providing a variable transmittance behavior is limited to only three specific wavelengths, alternating stacked layers of first and second dielectrics can provide the desired increase in transmittance in the waveguide direction even when the number of discrete values ​​of the percentage thickness variation is less (preferably significantly less) than the total number of layers. This is advantageous because such a coating can be simpler, cheaper, and more reliable to manufacture than a coating that includes a unique percentage thickness variation for each layer. This will be explained with reference to the first example below.

[0204] The first example includes 12 layers of dielectric. However, the percentage change in thickness of each layer from the first end to the second end of the layer has one of four discrete allowable values. In particular, the percentage change in thickness of each layer of the first dielectric is equal to the first value or the second value, and the percentage change in thickness of each layer of the second dielectric is equal to the third value or the fourth value. Therefore, the total number of layers of the first and second dielectrics (i.e., 12) is greater than the total number of discrete allowable values ​​(i.e., four). Figure 10C As shown, the transmission of the blue, green, and red wavelengths for which the coating is designed is acceptable. Figure 11 As shown, the transmittance of the coated waveguide does not perform acceptably at other wavelengths.

[0205] Figure 11 It is a curve graph. Figure 11 The Y-axis represents the transmittance. The X-axis represents the nth emission region along the first surface of the waveguide. The solid line 1102 represents the ideal transmittance of the first surface. The solid line 1102 appears different from Figure 9 The solid line is shown, but this is because Figure 11 The scale of the Y axis is different from Figure 9 The three dashed lines show the simulated transmittance of the waveguide of the first example for three different wavelengths of electromagnetic radiation for which the waveguide is not configured. The three dashed lines indicate that the transmittance of the coated waveguide does not follow the ideal behavior at the corresponding wavelengths. The wavelength 1104 deviates significantly from the ideal behavior.

[0206] Thus, a waveguide having the first example coating may not be acceptably transmissive for wavelengths outside the specific wavelengths that the waveguide coating is designed for. However, this is not critical for applications where those wavelengths are not transmitted through the waveguide (i.e., are not used to form an image).

[0207] Further examples of coatings can be found in GB patent application 2214069.3, which is incorporated herein by reference in its entirety.

[0208] Manufacturing method

[0209] The advantage of the layered coating disclosed herein is that it can be manufactured in a cheap, fast and reliable manner. Here, an example of such a method is disclosed. However, those skilled in the art will appreciate that other methods are also possible.

[0210] The method comprises the steps of providing a waveguide substrate comprising a pair of parallel surfaces arranged to provide a waveguide therebetween; and applying a plurality of layers of a first dielectric and a plurality of layers of a second dielectric to the waveguide substrate such that the layers of the first dielectric and the layers of the second dielectric are in an alternating configuration.

[0211] The apparatus for performing this method includes two sources of a first dielectric material (e.g., SiO2) and two sources of a second dielectric material (e.g., TiO2), a shadow mask comprising first through fourth trapezoidal apertures, and a device for moving the waveguide substrate relative to the shadow mask. Each aperture in the shadow mask is associated with a source of dielectric material. During the fabrication of each layer, dielectric material from one of the sources is configured to flow through one of the apertures in the shadow mask. The waveguide substrate is moved relative to the shadow mask (or vice versa) such that the shadow mask is positioned between the sources and the waveguide substrate. The waveguide substrate passes under the apertures, and a layer of dielectric material forms on the surface of the waveguide substrate. This is illustrated in FIG19 .

[0212] Figure 12 is a schematic cross-sectional view of a portion of an apparatus for manufacturing a waveguide according to the present disclosure, the cross-section being in the XY plane. Figure 12 The portion of the apparatus shown includes a first source of SiO2 and a shadow mask 2004 containing a first aperture 2006. Also shown is a waveguide substrate 2008 (in the form of a glass or Plexiglas block or plate). SiO2 material 2010 is configured to flow out of the first source 2002 and through the first aperture 2006 of the shadow mask 2004. The material flow is in the negative Y direction. The shape of the first aperture 2006 determines the shape of the SiO2 flow downstream of the shadow mask 2004. Figure 12 Not drawn to scale.

[0213] The device for moving the waveguide substrate 2008 (not shown) is arranged to move the waveguide substrate 2008 in a first plane perpendicular to the Y direction so that the waveguide substrate 2008 passes under the first hole 2006. In some embodiments, the movement is entirely in the X direction. However, in other embodiments, the waveguide substrate 2008 can be rotated in the first plane so that the movement is in the X direction and the Z direction.

[0214] exist Figure 12 In the example shown, the waveguide substrate 2008 has not yet passed under the first hole 2006, and therefore no dielectric coating is present on the waveguide substrate 2008. The dielectric coating is deposited on the substrate as the waveguide substrate passes under the first hole 2006 (in the X direction). Typically, to produce a complete layer, the waveguide substrate 2008 will need to pass under the first hole 2006 multiple times until the desired thickness is achieved.

[0215] Once the first layer 2010 has been formed, the waveguide substrate 2008 will be moved under one of the sources of a second dielectric material so that a second layer (of the second dielectric material) is formed on top of the first layer 2010 of the first dielectric material.

[0216] Figure 13 is a schematic diagram of the shadow mask 2004, the view is taken from the XZ plane (i.e., perpendicular to Figure 12(a view plane). The shadow mask includes four apertures, namely a first aperture 2006 (described above), a second aperture 2102, a third aperture 2104, and a fourth aperture 2106. The first and third apertures 2006 and 2104 are each connected to a source of a first dielectric material. The second and fourth apertures 2102 and 2106 are each connected to a source of a second dielectric material. Each aperture has a trapezoidal shape with a short side and a long side.

[0217] To make subsequent alternating layers of the first and second dielectric materials, the waveguide substrate 2008 is moved under the different holes in sequence. The order of the layers can be controlled based on the order of the holes that the waveguide substrate 2008 moves under. The waveguide substrate 2008 is rotated / moved relative to the shadow mask 2004 to pass under the different holes so that the waveguide substrate 2008 passes under the holes in the X direction and so that the short and long sides of the holes are spaced apart in the Z direction. In this way, the thickness of each deposited layer varies in the Z direction. The percentage change in thickness of a layer from the first end to the second end (in the Z direction) will depend on the percentage change in width of the short and long sides of the corresponding holes. This refers to Figure 13 Provide explanation.

[0218] Figures 14A to 14D 2008 are schematic cross-sectional views of four different first layers formed on the waveguide substrate 2008 . Figure 14A A layer 2202 is shown that is formed when the waveguide substrate 2008 passes under the first hole 2006. Figure 14B The layer 2204 formed when the waveguide substrate 2008 passes under the second hole 2102 is shown. Figure 14C The layer 2206 formed when the waveguide substrate 2008 passes under the second hole 2104 is shown. Figure 14D There is shown a layer 2208 that is formed when the waveguide substrate 2008 passes under the second hole 2106. As will be appreciated by the skilled artisan, the thickness profile of each of the layers 2202 to 2208 corresponds to the shape of the respective hole.

[0219] Specifically, layers 2202 and 2206 have a positive gradient from left to right because the widths of apertures 2006 and 2104 increase in the Z direction of the waveguide substrate as the shadow mask and waveguide substrate are rotated relative to each other. The percentage change in thickness of layer 2206 is greater than the percentage change in thickness of layer 2202 because the percentage change in width of aperture 2104 from its short side to its long side is greater than that of aperture 2006. Layers 2204 and 2208 have a negative gradient from left to right because the widths of apertures 2102 and 2106 decrease in the Z direction as the shadow mask and waveguide substrate are rotated relative to each other. The percentage change in thickness of layer 2204 is greater than the percentage change in thickness of layer 2208 because the percentage change in width of aperture 2102 from its short side to its long side is greater than that of aperture 2106.

[0220] As will be appreciated, the arrangement of a shadow mask 2004 having four differently shaped apertures, two apertures connected to a first dielectric material source, and two apertures connected to a second dielectric material source, provides a means for producing multiple layers of a first dielectric and multiple layers of a second dielectric arranged in an alternating configuration. Each layer of the first dielectric will have a percentage variation in thickness equal to either the first value or the second value, where all layers having the first value are associated with, for example, the first aperture 2006, and all layers having the second value are associated with, for example, the second aperture 2102. Each layer of the second dielectric will have a percentage variation in thickness equal to either the first value or the second value, where all layers having the third value are associated with, for example, the third aperture 2104, and all layers having the second value are associated with, for example, the fourth aperture 2106. In other words, a means for producing a layered coating according to the present invention is provided.

[0221] An advantage of this manufacturing method is that the waveguide substrate can be quickly and easily moved / rotated to pass under the apertures of the shadow mask 2004 as needed, thereby building up multiple alternating layers of first and second dielectric materials as desired. The number of unique shadow masks with different shapes determines the number of discrete values ​​of layer thickness percentage variation that can be achieved, so the thickness percentage variation of any particular layer can be controlled simply by selecting the aperture sequence. The absolute thickness of any layer can be controlled by controlling the speed at which the waveguide substrate passes under a particular shadow mask 2004 or by controlling the material flow rate.

[0222] It should be understood that the manufacturing methods disclosed herein are not limited to four holes and two sources of dielectric material. For example, increasing or decreasing the number of differently shaped shadow masks will simply have the effect of increasing or decreasing the discrete number of permissible percentage variations in the thickness values ​​of the layers that can be obtained.

[0223] Improved methods of coating application

[0224] In summary, a further improved coating design method is provided, comprising the following steps:

[0225] 1. Design the base structure, which is usually a multilayer mirror with RGB windows used in the lowest T% position. This step does not involve gradients.

[0226] 2. Apply a linear gradient on the multi-layer base structure and optimize the gradient so that the coating transmittance at different positions can meet any requirements.

[0227] The general idea is to use the gap between the RGB windows as a design freedom to help maintain a stable and synchronized increase in transmission within the RGB windows. Therefore, the design is very sensitive to gradients and small changes (a few percent) may significantly change the coating transmission.

[0228] In practice, the inventors found that it was difficult to adjust the shadow mask to meet the same gradient thickness as designed. There were several challenges:

[0229] • Adjusting the shadow mask is a time-consuming process that requires precision machining of the metal.

[0230] There is no simple relationship between gradient thickness and the physical gradient of the mask opening. To achieve a linear gradient thickness, the mask usually needs to have some nonlinearity. Approaching the desired gradient after several iterations is usually a process of trial and error.

[0231] In mass production, shadow masks degrade within a few weeks and require maintenance / re-adjustment. This increases the chances of small deviations in gradient thickness.

[0232] Typically, gradient masks are close to the design, but not exact. To help address these imperfect gradient masks, this paper discloses a "post-processing" coating optimization that does not require any hardware changes but can significantly improve coating performance. The method includes:

[0233] Fix the gradient (“coating function”) as is, i.e. accept small deviations without further optimization.

[0234] • Finding the optimal set of multilayer thicknesses that “takes full advantage” of a fixed gradient (“coating function”).

[0235] Prior to the optimization of the present disclosure, multilayer thicknesses were designed for an ideal gradient and therefore could not fit the actual gradient. This optimization found a set of (slightly) different thicknesses (an example of a "coating parameter") to work with the actual gradient (the measured "coating function").

[0236] Figure 15 Shows the use Figure 12 to 1 4 and described above, for applying a coating, such as the coating described above, to a waveguide substrate 2008.

[0237] First, calculate the ΔV at multiple locations along the length of the waveguide (e.g. Figure 5 The "bounce" points B0 to B8 or Figure 7 and 10A 1 to 11) of the emission region. Thus, a determination 3000 is performed of the number of coating layers and the profile of each layer to achieve the optimized transmittance (as described above), as well as the specific shadow mask 2004, waveguide substrate 2008 speed, and material flow rate required to apply the optimized layer formation (also as described above). This determination 3000 outputs an optimized value 3100.

[0238] Using these optimized values ​​3100, the various layers of coating are then applied to the waveguide substrate 2008 as described above in a forming step 3200. This forms a first coated waveguide. Given factors such as wear on the shadow mask 2004, it has been observed that the actual transmittance of the first waveguide will differ from the transmittance optimized during determination 3000. This is confirmed by measuring 3300 the thickness of the layers at the various locations used in determination 3000 (as described above, variations in the thickness of any layer at any point along the waveguide result in variations in transmittance). As described above, the measuring 3300 step can use data from a pass or fail evaluation of the coating. However, the present disclosure relates to using measured data to determine the actual coating function of the shadow mask, rather than simply evaluating a pass or fail.

[0239] Using the measured 3300 values, the optimization performed for the initial determination 3000 is repeated to account for differences between the simulated optimized waveguide and the waveguide actually produced in the forming step 3200. In this way, the values ​​generated by this re-optimization can be used to form each layer of the coating that maintains the desired optical properties while accounting for wear or other defects on the shadow mask 2004. Notably, the re-optimization exploits the degrees of freedom associated with the coating parameters (e.g., coating speed or minimum thickness) to provide better performance without changing the shadow mask.

[0240] In some embodiments of the method, an optimization loop may be formed, such as Figure 16 In this case, repeating the optimization 3400 generates a new set of values ​​3500 related to the updated waveguide substrate 2008 velocity and material flow velocity required to apply the updated layer formation. The desired profile of each layer remains the same to avoid having to replace a worn shadow mask 2004 with one having a different shape and / or unworn apertures.

[0241] The actual transmittance of the first coated waveguide at various points along the waveguide is then measured 3600. This is compared to the optimized transmittance of the optimized value 3100 in a comparison step 3700. If the actual transmittance is within a predetermined tolerance (i.e., within an acceptable error rate) of the optimized value 3100, then mass production 3800 of the waveguides begins or continues (until the shadow mask 2004 wears further and the process needs to be repeated). However, if the actual transmittance is not within the tolerance, a second coated waveguide is formed in a forming step 3200 using a new set of values ​​3500. The cycle of steps 3200, 3300, 3400, and 3600 is repeated until the tolerance is met. In this way, a group of waveguides is produced with the desired transmittance characteristics, regardless of wear of the shadow mask 2004, which introduces inaccuracies in the applied coating. For the avoidance of doubt, the present disclosure features the "actual" coating function for each shadow mask derived by measurement (e.g., using pass or fail test data) and using the degrees of freedom associated with the coating parameters to optimize performance and extend the life of the shadow mask. Figures 17 to 19C Describe the effectiveness of this approach.

[0242] Figure 17 Another method of applying the coating is shown. First, as in the above method, the thickness of the coating is calculated at multiple locations along the length of the waveguide (e.g., at Figure 5 The "bounce" points B0 to B8 or Figure 7 and 10A 1 to 11) of the emission region. Thus, a determination 4000 is performed of the number of coating layers and the profile of each layer to achieve the optimized transmittance (as described above), as well as a determination of the specific shadow mask 2004, waveguide substrate 2008 speed, and material flow rate required to apply the optimized layer formation (also as described above). This determination 4000 outputs an optimized value 4100.

[0243] Using these optimized values ​​4100, a first layer of coating is applied to the waveguide substrate 2008 as described above in a forming step 4200. As discussed with respect to the above method, given factors such as wear on the shadow mask 2004, it is expected that the actual transmittance of the first layer will differ from the transmittance optimized during the determination 4000. This is confirmed by measuring 4300 the thickness of the first layer at the various locations used in the determination 4000 (as described above, variations in thickness result in variations in transmittance).

[0244] Using the measured 4300 values, a further optimization 4400 is performed to produce a new set of values ​​4500 related to the updated waveguide substrate 2008 velocity and material flow velocity required to apply the second layer, while taking into account the differences between the simulated optimized first layer and the first layer actually produced in the forming step 4200. As with the above method, the expected profile of each layer remains the same to avoid having to replace a worn shadow mask 2004 with a shadow mask having a different shape and / or unworn holes.

[0245] Finally, in decision step 4600, if this is the last layer to be applied, the process ends and the coating is complete. However, if this is not the last layer, the next layer is formed in formation step 4200 using the new set of values ​​4500. The cycle of steps 4200, 4300, and 4400 is repeated until the coating is complete. In this way, a waveguide having the desired transmittance characteristics is produced regardless of wear of the shadow mask 2004, which introduces inaccuracies when applying each layer of coating.

[0246] Examples of coatings applied using the improved method

[0247] In summary, FIG18 shows a simulation of the original multilayer thickness with some realistic, deviating gradient thicknesses. Figure 18C It shows that half of the gradient thickness (even layers) is no longer linear, and the actual gradient amplitude is also higher than the designed gradient amplitude. Figure 18A , odd layers) remain linear in this example. As a result, Figure 18C As shown, the RGB transmission deviates from the target line 5002. In summary, in FIG19 , all gradient percentages (shadow mask / "coating function") remain unchanged, but the layer thicknesses ("coating parameters") are reoptimized, i.e., the curves shift slightly up / down in the lower left / right graphs, but retain the same shape. After optimization, the graded RGB transmission is closer to the original target. Once the optimization algorithm is finalized, the optimization can be run automatically with any gradient input (within a certain range) and return the optimal thickness in near real time.

[0248] More specifically, Figures 18A to 18C A real-world example of a coating applied using known methods involves a shadow mask 2004 that has worn, causing inaccuracies. The coating in this example includes 30 alternating layers of two different dielectric materials. The layers are numbered 1 to 30, so that light emitted from the waveguide passes through each of the layers 1 to 30 in sequence.

[0249] Figure 18A and 18BThe diagram shows how the actual measured thickness of each layer varies with distance along the first surface of the waveguide (i.e., from the first end to the second end of each layer). According to the present disclosure, these actual thicknesses differ from the specified thicknesses. That is, they differ from the designed or required thicknesses of the layers. Such deviations may be due to aging of the shadow mask. The Y-axis represents thickness, and the X-axis represents position along the waveguide. The numbers 1 to 9 on the X-axis represent the emission areas of the first surface.

[0250] Coated waveguides according to the present disclosure will typically behave differently at different wavelengths. As will be appreciated by those skilled in the art, a combination of blue, green, and red light sources can be used to provide a full-color image (i.e., light having three different wavelengths). For example, in many holographic systems, blue, green, and red light sources are used to produce a full-color image. If a waveguide produced by the present disclosure is suitable for use in such a system, the transmittance of the coated first surface at each desired wavelength should substantially follow Figure 9 Ideal transmittance shown.

[0251] Figure 18C is a graph showing the transmittance of the first surface of the waveguide of this example. Figure 18C The transmittance of layers L1 to L30 can be measured optically or obtained through simulation. The Y-axis represents the transmittance. The X-axis represents the nth emission region along the first surface of the waveguide. Figure 18C The solid line (unbroken line) 5002 represents the ideal transmission behavior (also Figure 9 The three dashed (interrupted) lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. Figure 18C The three wavelengths shown are associated with blue laser light 5004, green laser light 5006, and red laser light 5008. As can be seen, the three wavelengths 5004, 5006, and 5008 differ significantly from the ideal transmission behavior 5002 in multiple emission regions. This is caused by poor performance (e.g., wear) on the shadow mask 2004, as described above.

[0252] Figures 19A to 19C Involving the application of the method according to the present disclosure Figures 18A to 18C A real example of a coating that has been further optimized according to the present disclosure. This example coating includes 30 alternating layers of two different dielectric materials. The layers are numbered from 1 to 30 so that light emitted from the waveguide passes through each of layers 1 to 30 in sequence.

[0253] Figure 19A and 19B The graph shows how the actual measured thickness of each layer varies with distance along the first surface of the waveguide (i.e., from the first end to the second end of each layer) after re-optimization (or second optimization step) according to the present disclosure. The Y-axis represents thickness and the X-axis represents position in the waveguide direction. The numbers 1 to 9 on the X-axis represent the emission areas of the first surface. It can be seen that the thickness of each layer L1 to L30 varies with respect to the first surface of the waveguide. Figure 18A and 18B The corresponding thicknesses shown in are offset.

[0254] For the avoidance of doubt, Figure 19A and 19B The layers L1 to L30 shown have been determined by using at least one measured coating function after a first coating run and allowing the coating parameters to float during design in order to improve Figure 19C The achieved transmittance is shown.

[0255] Figure 19C is a graph showing the transmittance of the first surface of the waveguide of this example. The Y-axis represents the transmittance. The X-axis represents the nth emission region along the first surface of the waveguide. Figure 19C The solid line (unbroken line) 6002 represents the ideal transmission behavior (also Figure 9 The three dashed (interrupted) lines show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. Figure 19C The three wavelengths shown are related to blue laser 6004, green laser 6006 and red laser 6008. It can be seen that the thickness of each layer L1 to L30 is adjusted so that the wavelengths 6004, 6006, 6008 are much thicker than those generated by known methods (such as Figure 18C ) closer to the ideal transmission characteristic 6002. This improved transmittance is produced without replacing or repairing the worn shadow mask 2004.

[0256] Additional Features

[0257] The embodiments relate to electrically activated LCOS spatial light modulators by way of example only. The teachings of the present disclosure may equally be implemented on any spatial light modulator capable of displaying computer-generated holograms according to the present disclosure, such as any electrically activated SLM, optically activated SLM, digital micromirror device, or microelectromechanical device.

[0258] In some embodiments, the light source is a laser, such as a laser diode. In some embodiments, the detector is a photodetector, such as a photodiode. In some embodiments, the light receiving surface is a diffuser surface or screen, such as a diffuser. The holographic projection system of the present disclosure can be used to provide an improved head-up display (HUD). In some embodiments, a vehicle is provided, which includes a display system installed in the vehicle to provide a HUD. The vehicle can be a motor vehicle, such as a car, truck, van, delivery truck, motorcycle, train, airplane, ship, or boat.

[0259] The quality of the holographic reconstruction can be affected by the so-called zero-order problem, which is a consequence of the diffraction properties of the pixelated spatial light modulators used. This zero-order light can be considered "noise" and includes, for example, specularly reflected light and other unwanted light from the SLM.

[0260] In the example of Fourier holography, this "noise" is concentrated at the focal point of the Fourier lens, resulting in a bright spot at the center of the holographic reconstruction. The zero-order light can simply be blocked out, however this means replacing the bright spot with a dark spot. Some embodiments include an angle-selective filter to remove only the collimated light of the zero order. Embodiments also include methods for managing the zero order as described in European Patent 2,030,072, which is incorporated herein by reference in its entirety.

[0261] In some embodiments, the size of the hologram (the number of pixels in each direction) is equal to the size of the spatial light modulator so that the hologram fills the spatial light modulator. That is, the hologram uses all the pixels of the spatial light modulator. In other embodiments, the hologram is smaller than the spatial light modulator. More specifically, the number of hologram pixels is less than the number of light modulation pixels available on the spatial light modulator. In some of these other embodiments, a portion of the hologram (i.e., a continuous subset of the pixels of the hologram) is repeated in unused pixels. This technique may be referred to as "tiling," in which the surface area of ​​the spatial light modulator is divided into multiple "tiles," each representing at least a subset of the hologram. Therefore, the size of each tile is smaller than the size of the spatial light modulator. In some embodiments, "tiling" techniques are implemented to improve image quality. Specifically, some embodiments implement tiling techniques to minimize the size of image pixels while maximizing the amount of signal content that enters the holographic reconstruction. In some embodiments, the holographic pattern written to the spatial light modulator includes at least one complete tile (i.e., a complete hologram) and at least a small portion of the tile (i.e., a continuous subset of the pixels of the hologram).

[0262] In an embodiment, only primary playback fields are utilized, and the system includes physical blocks, such as baffles, arranged to limit the propagation of higher-level playback fields through the system.

[0263] In embodiments, the holographic reconstruction is in color. In some embodiments, a method known as spatially separated colors "SSC" is used to provide color holographic reconstruction. In other embodiments, a method known as frame sequential color "FSC" is used.

[0264] The SSC method uses three spatially separated arrays of light-modulating pixels for three monochrome holograms. The advantage of the SSC method is that the images can be very bright because all three holographic reconstructions can be formed simultaneously. However, if three spatially separated arrays of light-modulating pixels are provided on a common SLM due to space limitations, the quality of each monochrome image will be suboptimal because each color only uses a subset of the available light-modulating pixels. As a result, a relatively low-resolution color image is provided.

[0265] The FSC method can use all the pixels of a common spatial light modulator to display three monochrome holograms in sequence. The monochrome reconstruction cycle (e.g., red, green, blue, red, green, blue, etc.) is fast enough that a human viewer perceives a multicolor image from the integration of the three monochrome images. The advantage of FSC is that the entire SLM can be used for each color. This means that the three color images produced are of optimal quality because all the pixels of the SLM are used for each color image. However, a disadvantage of the FSC method is that the brightness of the composite color image is lower than that of the SSC method - about 3 times - because each monochrome illumination event can only occur for one-third of the frame time. This shortcoming can be addressed by overdriving the laser or using a more powerful laser, but this requires more power, resulting in higher cost and increased system size.

[0266] While the examples describe illuminating the SLM with visible light, those skilled in the art will appreciate that the light source and SLM can also be used to direct infrared or ultraviolet light, such as disclosed herein. For example, those skilled in the art will be aware of techniques for converting infrared and ultraviolet light into visible light for the purpose of providing information to a user. For example, the present disclosure extends to the use of phosphors and / or quantum dot technology for this purpose.

[0267] Some of the devices describe 2D holographic reconstructions by way of example only. In other devices, the holographic reconstruction is a 3D holographic reconstruction. That is, in some devices, each computer-generated hologram forms a 3D holographic reconstruction.

[0268] The methods and processes described herein may be embodied on a computer-readable medium. The term "computer-readable medium" includes media arranged to store data temporarily or permanently, such as random access memory (RAM), read-only memory (ROM), buffer memory, flash memory, and cache memory. The term "computer-readable medium" should also be taken to include any medium or combination of media that can store instructions for execution by a machine, such that when the instructions are executed by one or more processors, the machine performs, in whole or in part, any one or more of the methods described herein.

[0269] The term "computer-readable medium" also encompasses cloud-based storage systems. The term "computer-readable medium" includes, but is not limited to, one or more tangible and non-transitory data storage repositories (e.g., data volumes) in the example form of solid-state memory chips, optical disks, magnetic disks, or any suitable combination thereof. In some example embodiments, instructions for execution may be conveyed by a carrier medium. Examples of such carrier media include transient media (e.g., a propagated signal conveying the instructions).

[0270] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the scope of the appended claims. This disclosure covers all modifications and variations within the scope of the appended claims and their equivalents.

Claims

1. A method of forming a transmissive coating for a waveguide, wherein: The transmissive coating comprises a plurality of layers, and the method comprises the steps of: a. determining a first coating parameter and a coating function for each layer to optimize the transmittance at a plurality of locations along the waveguide for a plurality of different wavelengths, the coating function being selected from a plurality of allowable coating functions; b. forming a plurality of layers using determined coating parameters and coating functions; c. measuring the thickness of at least one layer at each of a plurality of locations, wherein the measurements indicate that the coating function deviates from the function selected during the optimization of step a; and d. Determining second coating parameters of the at least one layer by repeating the optimization of step a using the coating function derived from the measurement of step c.

2. The method according to claim 1, wherein Each coating function is a percentage change in layer thickness along the length of the waveguide from a first end of the waveguide to a second end of the waveguide.

3. The method according to claim 2, wherein: The number of permissible coating functions is between two and six, optionally between two and four, optionally four.

4. The method according to claim 2 or 3, wherein: Each determined coating function is linear, optionally wherein the measurement of step c indicates that the coating function is non-linear.

5. A method as claimed in any preceding claim, wherein The first coating parameter relates to the thickness of the layer at its thinnest point.

6. A method as claimed in any preceding claim, wherein The forming of the plurality of layers of step b includes controlling the flow of the coating material toward the waveguide using a shadow mask.

7. The method according to claim 6, wherein: The first coating parameter and the second coating parameter are one of: a rate at which the coating material flows towards the waveguide; or a rate at which the waveguide moves through the flow of coating material.

8. The method of claim 7, wherein: Step a further comprises determining a third coating parameter, and step d further comprises determining a fourth coating parameter, the third coating parameter and the fourth coating parameter being the other of: a rate of coating material flow towards the waveguide; or a rate at which the waveguide moves through the coating material flow.

9. A method as claimed in any preceding claim, wherein The plurality of layers includes at least one dielectric.

10. A method as claimed in any preceding claim, wherein The forming of multiple layers in step b includes forming alternating layers of a first material and a second material; optionally, wherein the first material is a first dielectric, the second material is a second dielectric, the first dielectric is a first oxide, fluoride, sulfide or nitrate of a first transition metal or semiconductor, and the second dielectric is a second oxide, fluoride, sulfide or nitrate of a second transition metal or semiconductor, and / or wherein the refractive index difference between the first material and the second material is greater than 0.

4.

11. A method as claimed in any preceding claim, wherein The multiple different wavelengths include a first wavelength, a second wavelength and a third wavelength. Optionally, the first wavelength is in the range of 630-670 nm, the second wavelength is in the range of 500-540 nm, and the third wavelength is in the range of 430-470 nm.

12. A method as claimed in any preceding claim, wherein The optimized transmittance T(n) at each of a plurality of locations along the waveguide satisfies the following equation: where L is the optical loss factor of the waveguide material.

13. A method as claimed in any preceding claim, wherein The optimization of steps a and d also includes taking into account the transmittance of another transmissive coating on the surface opposite to the applied transmissive coating.

14. A method as claimed in any preceding claim, wherein The deviated coating function is determined by fitting the original coating function to the measured thickness.

15. A method as claimed in any preceding claim, wherein The measurement in step c includes measuring the thickness of each layer.

16. A method as claimed in any preceding claim, wherein The iterative optimization of step d includes adjusting the coating parameters of each layer at each of the plurality of locations.

17. The method of any preceding claim, further comprising the steps of: e. forming or simulating a plurality of layers using the deviated coating function and the adjusted coating parameters of step d; f. determining or simulating the transmittance at multiple locations along the waveguide for multiple different wavelengths; as well as g. Repeat steps b to f until the determined / simulated transmittance of step f is within the tolerance of the optimized transmittance of step a.

18. A transmissive coating for a waveguide formed using the method of any preceding claim.

19. A waveguide comprising a transmissive coating formed using the method of any one of claims 1 to 21, optionally further comprising a reflective coating on a surface opposite the transmissive coating.

20. A holographic system comprising: a display device arranged to display a hologram of an image and output spatially modulated light in accordance with the hologram; as well as The first waveguide of claim 19; Optionally, a second waveguide is also included.

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