Waveguide coating optimization

Abstract

To provide a method of forming a transmission coating for a waveguide.SOLUTION: The transmission coating includes multiple layers. The method includes: a step a of determining a first coating parameter and a coating function for each layer to optimize the transmissivity at a plurality of locations along the waveguide for a plurality of different wavelengths, the coating function chosen from a plurality of allowable coating functions; a step b of forming the plurality of layers using the determined coating parameters and coating functions; a step c of measuring a thickness of at least one layer at each of the locations, the measurements indicating that the coating function deviates from that selected during the optimization of step a; and finally a step d of determining a second coating parameter for at least one layer by repeating the optimization of step a using the coating function derived from the measurements of step c.SELECTED DRAWING: Figure 15

Description

[Technical Field]

[0001] The present disclosure relates to pupil dilation or wavefront replication. More specifically, the present disclosure relates to a waveguide, a display system including at least one waveguide according to the present disclosure, a method of wavefront replication using at least one waveguide, and a method of guiding a wavefront, such as a holographic wavefront. Even more specifically, the present disclosure relates to a method for improving the uniformity of a wavefront replica output by a waveguide, and optical components (such as optical layers, dielectric layers, or dielectric stacks) for a waveguide. The present disclosure also relates to a method for forming a transmission coating for a waveguide, a method for designing a transmission coating for a waveguide, and a method for manufacturing a transmission coating for a waveguide. The transmission coating may be a graded transmission coating. [Background technology]

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

[0003] Computer-generated holography can numerically simulate interference processes. Computer-generated holograms can be calculated using techniques based on mathematical transforms, such as the Fresnel transform or the Fourier transform. These types of holograms are sometimes called Fresnel / Fourier transform holograms, or simply Fresnel / Fourier holograms. Fourier holograms can be viewed as a Fourier domain / planar representation of an object, or a frequency domain / planar representation of an object. Computer-generated holograms can be calculated, 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 incident light. Light modulation can be achieved using, for example, electrically addressable liquid crystals, optically addressable liquid crystals, or micromirrors.

[0005] Spatial light modulators are typically composed of multiple individually addressable pixels, also called cells or elements. The light modulation scheme may be binary, multilevel, or continuous. Alternatively, the device may be continuous (i.e., not pixelated), and thus the light modulation may be continuous across the device. Spatial light modulators may be reflective, meaning that modulated light is output through reflection. Spatial light modulators may also be transmissive, meaning that modulated light is output through transmission.

[0006] The systems described herein can be used to provide holographic projectors, which have applications in head-up displays (HUDs). Summary of the Invention

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

[0008] Broadly, this disclosure relates to image projection. This disclosure relates to an image projector comprising a method of image projection and a display device. This disclosure also relates to a projection system comprising an image projector and a viewing system that projects or relays light from the display device to the viewing system. This disclosure is equally applicable to monocular and binocular viewing systems. The viewing system may include one or both eyes of a viewer. The viewing system comprises an optical element having optical power (e.g., a lens / lenses in a human eye) and a display surface (e.g., the retina of a human eye). The projector is sometimes 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 image is formed on the display surface or perceived by the viewer. In some embodiments, the image is a virtual image, and the display surface is sometimes referred to as a virtual image surface. In other embodiments, the image is a real image formed by holographic reconstruction, and the image is projected or relayed to the display surface. The image is formed by illuminating a diffraction pattern (e.g., a hologram) displayed on the display device.

[0009] Display devices are made up of pixels, which diffract light, and according to well-known optics, the size of the pixel (and other factors such as the wavelength of the light) determines the magnitude of the maximum diffraction angle.

[0010] In embodiments, the display device is a spatial light modulator, such as a liquid crystal on silicon ("LCOS") spatial light modulator (SLM). Light propagates from the LCOS toward a display 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, magnification techniques may be used to expand the range of available diffraction angles beyond the conventional maximum diffraction angle of the LCOS.

[0011] In some instances, an image (formed from a displayed hologram) is propagated to the eye, e.g., spatially modulated light of an intermediate holographic reconstruction / image formed in free space between the display device and the viewer or on a screen or other light-receiving surface may be propagated to the viewer.

[0012] In some other examples, the hologram itself (light) is propagated to the eye. For example, the hologram's spatially modulated light (not yet fully converted into a holographic reconstruction, i.e., an image), which may informally be referred to as "encoded" by the hologram, is propagated directly to the viewer's eye. A real or virtual image may be perceived by the viewer. In these embodiments, no intermediate holographic reconstruction / image is formed between the display device and the viewer. In these embodiments, the lens of the eye is sometimes said to perform the hologram-to-image conversion or recombination. The projection system or light engine may be configured so that the viewer effectively looks directly at 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 the eye or other viewing object / system varies depending on the distance between the display device and the viewing object. For example, at a viewing distance of one meter, only a small angular range from the LCOS passes through the eye's pupil to form an image on the retina at a particular eye position. The angular range of light rays propagating from the display device that can pass through the eye's pupil to form an image on the retina for a given eye position determines the portion of the image that is "visible" to the viewer. In other words, not all portions of the image are visible from any one point on the viewing surface (e.g., any one eye position within an observation window such as an eye movement box).

[0014] In some embodiments, the image perceived by the viewer is a virtual image displayed upstream of the display device, meaning the viewer perceives the image as being farther away than the display device. Conceptually, the viewer can think of the virtual image as being viewed through a "display device-sized window," which may be very small, such as 1 cm in diameter, and viewable at a relatively large distance, such as 1 meter. The user also sees the display device-sized window through the pupil of their eye, which may also be very small. Thus, the field of view is narrowed, and the specific angular range that can be seen is highly dependent on the position of the eyes at any given time.

[0015] Pupil expanders address the problem of increasing the angular range over which light rays propagating from a display device can successfully pass through the eye's pupil to form an image. Display devices are typically (relatively) small and the projection distance is (relatively) large. In some embodiments, the projection distance is at least one order of magnitude, e.g., at least two orders of magnitude, larger than the diameter or width of the entrance pupil and / or aperture of the display device (i.e., the size of the pixel array).

[0016] Using a pupil expander, the viewing area (i.e., the user's eyebox) is expanded laterally, allowing the user to see the image while still allowing some eye movement. As will be appreciated by those skilled in the art, in an imaging system, the viewing area (user's eyebox) is the area in which the observer's eyes can perceive the image. This disclosure particularly relates to non-infinite virtual image distances, i.e., near-field virtual images, but applies equally to virtual images formed at infinity or real images formed downstream of a display device / hologram.

[0017] The display device may have an active or viewing area with a first dimension less than 10 cm, e.g., less than 5 cm or less than 2 cm. The propagation distance between the display device and the viewing system may be 1 m or more, e.g., 1.5 m or more or 2 m or more. The light propagation distance in the waveguide may be up to 2 m, e.g., up to 1.5 m or up to 1 m. The method can receive an image and determine a corresponding hologram of sufficient quality in less than 20 ms, e.g., less than 15 ms or less than 10 ms.

[0018] In some embodiments, a hologram, described solely as an example of a diffractive or holographic light field or wavefront according to the present disclosure, is configured to route light into multiple channels, each channel corresponding to a different portion (i.e., subarea) of an image. The hologram may be displayed, or otherwise represented, on a display device, such as a spatial light modulator. When displayed on an appropriate display device, the hologram can spatially modulate light that can be converted into an image by a viewing 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 with image information by the hologram. The light in each channel is said to be in the hologram domain, rather than the image or spatial domain. In some embodiments, the hologram is a Fourier or Fourier transform hologram, and therefore the hologram domain is the Fourier or frequency domain. The hologram may also be a Fresnel or Fresnel transform hologram. Holograms are described herein as routing light into multiple hologram channels, each corresponding to a respective image subregion, simply to reflect that the image that can be reconstructed from the hologram has a finite size and can be arbitrarily divided into multiple image subregions. Importantly, the hologram in this example is characterized by how it distributes its image content when illuminated. Specifically, the hologram divides the image content by angle; that is, each point on the image is associated with a unique ray angle in the spatially modulated light formed by the hologram when illuminated—or, at least, a unique pair of angles, since holograms are two-dimensional. For the avoidance of doubt, the behavior of this hologram is unconventional. The spatially modulated light formed by this special type of hologram, when illuminated, may be arbitrarily divided into multiple hologram channels, each defined by a range of (two-dimensional) ray angles.From the foregoing, it will be appreciated that any hologram channel (i.e., subrange of ray angles) that can be considered in the spatially modulated light is associated with a respective portion or subregion of the image. That is, all of the information necessary to reconstruct that portion or subregion of the image is contained in the subrange of angles of the spatially modulated light formed from the hologram of the image. When the spatially modulated light is observed as a whole, there is not necessarily evidence of multiple spatially separated light channels. However, in some configurations, multiple spatially separated hologram channels are formed by intentionally leaving the region of the target image where the hologram is calculated blank or empty (i.e., no image content is present).

[0019] Nevertheless, the hologram can be identified. For example, if only a successive portion or subregion of the spatially modulated light formed by the hologram is reconstructed, only a subregion of the image will be visible. If a different successive portion or subregion of the spatially modulated light is reconstructed, a different subregion of the image will be visible. A further identifying feature of this type of hologram is that the cross-sectional shape of the hologram channel substantially corresponds to (i.e., is substantially the same as) the shape of the entrance pupil, although the sizes may differ, at least in 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. These are exemplary methods for characterizing or identifying this type of hologram, although other methods may be used. In summary, the holograms disclosed herein are characterized and identifiable by how the image content is distributed within the light encoded by the hologram. Again, for the avoidance of doubt, references herein to holograms configured to direct light or angularly split an image into multiple holographic channels are intended to be exemplary only, and the present disclosure is equally applicable to pupil dilation of any type of wavefront or light field, including any type of diffraction or diffracted light field.

[0020] Generally, disclosed herein is a system for providing pupil dilation of an input light field or wavefront, where the input light field is optionally a diffracted or holographic light field including diverging ray bundles. As described above, pupil dilation (which may also be referred to as "image duplication" or "duplication" or "pupil duplication") allows an observer to expand the size of the area in which the image can be seen (or the observer's eye can receive the light of a hologram forming the image) by creating one or more replicas of the input light beam (or ray bundle). Pupil dilation can be provided in one or more dimensions. For example, two-dimensional pupil dilation can be provided, with each dimension substantially orthogonal to each other. In embodiments in which the wavefront is a holographic wavefront, this process can be described as hologram duplication.

[0021] The system can be provided in a compact and streamlined physical form, making it suitable for a wide range of real-world applications, including those where space is at a premium and real estate is at a premium, such as implementation in head-up displays (HUDs) in vehicles and automobiles.

[0022] In this disclosure, the term "replica" is used simply to reflect that spatially modulated light is split and complex light fields or wavefronts are directed along multiple different optical paths. The term "replica" is used to refer to each occurrence or instance of a complex light field or wavefront after a replication event, such as partial reflection / transmission by a pupil dilator. Each replica travels along a different optical path. Some embodiments of the present disclosure relate to light encoded with a hologram rather than an image, i.e., 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 complex light field associated with the propagation of holographically encoded light varies with propagation distance. The use of the term "replica" here is independent of propagation distance; therefore, two branches or paths of light associated with a replication event are still referred to as "replicas" of each other, even if the branches have different lengths, and the composite light field evolves differently along each path. In other words, two composite light fields are still considered "replicas" according to the present disclosure, even if they are associated with different propagation distances, as long as 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 or direct a light field or wavefront between a pair of parallel surfaces. This can be achieved by internal reflection between the parallel surfaces. The first surface of the pair can be partially transflective. The second surface of the pair can be reflective. Thus, the light field is split for each internal reflection at the first surface, and multiple replicas of the light field are transmitted through the region of the first surface that forms the output port of the waveguide. Thus, the observation window (and eyebox) is expanded by the waveguide.

[0024] The intensity and spectrum of each successive replica emitted by the waveguide are required to be substantially constant from replica to replica. For example, the integral of the light intensity of each replica is substantially constant, the average light intensity of each replica is substantially constant, and / or the distribution of light intensity of each replica is 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 a spatially uniform emission. Spatially uniform replicas advantageously reduce or minimize variations in brightness of the image (or different regions thereof) perceived by an observer moving around the (magnified) viewing window. Furthermore, the overall quality of the hologram received by the observer (and / or the resulting image perceived by the observer) may be improved, especially when the hologram contains light of multiple different wavelengths.

[0025] The intensity of light guided between the first and second surfaces of a waveguide decreases each time the optical field is split at the first surface. Suboptimal waveguides are typically constructed with a first surface that has a constant reflectivity, resulting in a decrease in intensity for each successive replica. In other words, such conventional waveguides do not provide spatially uniform radiation.

[0026] A graded coating can be applied to a waveguide to vary the reflectivity, and therefore the transmittance, of the first surface. In particular, the coating can be arranged to increase the transmittance of the first surface in the waveguiding direction. The graded coating can be arranged so that the increase in the transmittance of the first surface in the waveguiding direction compensates for (e.g., at least partially compensates for) the decrease in the intensity of the guided light. However, current graded coatings often result in significant absorption losses of the guided light. Furthermore, these coatings typically offer very limited control over their spectral performance, which is particularly disadvantageous when the guided light contains multiple wavelengths. While some improved graded coatings exist, they are expensive, time-consuming, and complex to fabricate, and generally cannot be manufactured reliably. For example, such coatings can be constructed from multiple (often 20 or more) layers of dielectric material, each with a different rate of change in thickness from the first end to the second end of the layer. Such complex layer structures may be required to provide substantially spatially uniform emission across the visible spectrum, but are time-consuming and difficult to manufacture reliably (e.g., requiring the placement of a moving grader within the coating chamber).

[0027] The present disclosure addresses the technical challenge of providing spatially uniform radiation from a waveguide pupil dilator, with each replica having a substantially similar intensity and spectrum. The present disclosure proposes an improved waveguide pupil dilator that provides substantially uniform radiation at specific wavelengths, such as at least red, green, and blue wavelengths. The first surface of the waveguide includes multiple alternating layers of first and second dielectrics with different refractive indices. Instead of each layer having a unique thickness gradient, the present disclosure provides each dielectric layer with a thickness gradient having one of a discrete number of values, where the number of discrete values ​​is less than the total number of layers. In some embodiments, the number of discrete values ​​or allowable values ​​is four or less. In some embodiments, the number of layers is at least twice the number of discrete values.

[0028] Multilayer structures obtained using conventional design techniques are highly complex and not suitable for industrial scale-up. One source of complexity is the need to achieve uniformity at three different wavelengths. This design process was rethought, with emphasis placed on limiting the required manufacturing methods in ways that simplify them and mitigating them in other ways that do not affect the imaging (e.g., holographic) process. Particular emphasis was placed on simplifying the required coating machines. Limiting the number of different gradients used in the stack (e.g., reducing it to less than five, or even to four or three) and introducing degrees of freedom in the intermediate wavelengths (e.g., between the three hologram wavelengths) can achieve optical performance sufficient for replicating three-color holograms. Reducing the number of different grading tools significantly reduces manufacturing costs.

[0029] Compared to conventional methods that require the production of stacks in which each layer has its own inherent thickness gradient, faster and more reliable manufacturing methods can be used to produce the stacks of the present disclosure. By limiting the design of the waveguide coating to consider only certain regions of the visible spectrum, such alternating stacks according to the present disclosure can be configured to provide desirable optical performance, such as spatially uniform emission and low absorption losses at those wavelengths (but not necessarily at other wavelengths). Thus, the waveguides of the present disclosure may be particularly suited to applications that guide light at specific wavelengths rather than the entire optical spectrum. For example, many applications require spatially uniform emission of red, green, and / or blue light from the waveguide, but may not require other wavelengths (such as the yellow region of the spectrum). Such applications include head-up displays. The waveguides of the present disclosure may be suitable for such applications. As will be appreciated by those skilled in the art, red, green, and blue light can be used to generate full-color images.

[0030] According to a first example, a waveguide is provided, the waveguide comprising a pair of parallel / complementary surfaces arranged to provide waveguiding therebetween, the first of the pair of parallel surfaces comprising a plurality of first dielectric layers and a plurality of second dielectric layers arranged in an alternating configuration.

[0031] Each of the first and second dielectric layers has a first end and a second end. The first end is the (optical) input end, and the second end is the (optical) output end or the end of the output port / window of the final replica. The rate of change in thickness from the first end to the second end of each layer is one of a plurality of discrete values ​​(e.g., allowable values). The total number of first and second dielectric layers 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, optionally greater than 0.5.

[0032] Unless otherwise specified, the "rate of change in thickness" of a layer in this specification refers to the rate of change in thickness of the layer from a first end of the layer to a second end of the layer. The rate of change in thickness of a layer is 100 x (t f -t i ) / t i and t i is the thickness of each layer at the first end, and t f is the thickness of each layer at the second end.

[0033] Generally, each layer of the multiple layers is parallel to the other layers. The first end of each layer is aligned with the first end of the other layers, and the second end of each layer is aligned with the other layers. In other words, each layer has substantially the same length and / or width as the other layers, but may have a different thickness or depth. Multiple layers of first and second dielectrics are sometimes referred to as a stack of layers, or simply a dielectric stack.

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

[0035] As used herein, "multiple discrete values" refers to multiple values ​​that are different from one another. In other words, none of the multiple discrete values ​​is the same as any other discrete value. The magnitude and / or polarity of each discrete value may be different. The discrete values ​​may be referred to as "acceptable" or "predetermined" values. The rate of change in thickness of each layer may be selected during or determined by the manufacturing process. For example, if the multiple layers on the first surface of the waveguide are fabricated or processed using shadow masks, the rate of change in thickness of each layer may be related to the shape of the shadow mask, such that each discrete value is associated with a respective shadow mask. Those skilled in the art will understand that "acceptable" or "predetermined" discrete values ​​can take any appropriate value that provides the desired optical properties in the context of a particular multilayer structure of first and second dielectrics, and that appropriate values ​​can be calculated or determined, for example, using simulation. Each discrete value may be positive or negative. A positive value means that the thickness increases from the first end to the second end, and a negative value means that the thickness decreases from the first end to the second end.

[0036] Each layer has a thickness change rate equal to one of a plurality of discrete values. Because the number of layers is greater than the number of discrete values, at least two of the layers have the same thickness change rate from their respective first ends to their respective second ends. In some embodiments, two or more, optionally four or more, optionally six or more, optionally eight or more, optionally ten or more of the plurality of layers may have the same thickness change rate from their respective first ends to their respective second ends (and thus may be associated with the same discrete value). In some embodiments, layers with the same thickness change rate as each other are layers of the same dielectric (i.e., all layers with a particular thickness change rate are layers of the first dielectric or layers of the second dielectric).

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

[0038] The minimum thickness of each of the first and second dielectric layers, as well as the discrete values ​​of the thickness change rate, can be selected to provide the waveguide with desired optical properties, particularly the desired transmission behavior that results in spatially uniform radiation. These parameters depend, among other things, on the material properties (particularly the refractive index) of the first and second dielectrics, the angle of incidence of the light entering the waveguide, the wavelength of the incident light, and the distance between the pair of parallel faces of the waveguide. As will be appreciated by those skilled in the art, there are multiple (usually relatively many) arrangements of layers that will provide the waveguide with the desired optical properties. However, common to all of these arrangements is the advantage that the layered structure of the first face provides the desired optical properties and can be manufactured quickly, inexpensively, and reliably.

[0039] One example of a fast, inexpensive, and reliable method for fabricating the first and second dielectric layers is to deposit the respective dielectric materials onto a waveguide substrate to form the layers. A shadow mask can be used to control the flow of the dielectric material onto the substrate. Preferably, a trapezoidal shadow mask can be used. The rate of change in thickness of each layer is determined by the shape of the mask, and the total thickness of each layer can be determined by the length of time the dielectric material flows. If the mask is trapezoidal, the rate of change in thickness of each layer can correspond to the rate of change from the short base to the long base of the trapezoidal shape of the shadow mask. Different masks can be associated with each discrete value. For example, if there are first through fourth rate of change values, four different masks can be used to fabricate the layers of the coating. This has the advantage that the waveguide substrate simply needs to be moved between different material sources with different masks.

[0040] The plurality of discrete values ​​may consist of two or more (acceptable) discrete values, optionally three or more (acceptable) discrete values, optionally four or more (acceptable) discrete 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 ​​is significantly less 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 ​​includes a first value, a second value, and a third value. Each layer of the first dielectric can have a thickness change rate equal to either the first value or the second value. In other words, there are only two options for the thickness change rate of each layer of the first dielectric.

[0042] At least one layer of the second dielectric may have a thickness variation rate equal to a third value. When each layer of the first dielectric has either the first value or the second value, this means that at least one layer of the second dielectric has a thickness variation rate that is different from all layers of the first dielectric.

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

[0044] Preferably, the rate of change in thickness of each of the first and second dielectric layers may be constant. In other words, each layer may have a linear profile. It may be easier to manufacture dielectric layers with linear profiles. Furthermore, those skilled in the art will understand that it may be easier to calculate / determine the individual acceptable values ​​for a stack of layers with linear profiles.

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

[0046] The internal angle of incidence at each emission zone 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., wavelengths other than the first, second, and third visible wavelengths), the transmittance of the first surface may or may not increase in the direction of waveguiding. As previously discussed, the waveguides of the present disclosure may be particularly advantageous for guiding light at discrete wavelengths rather than guiding light having a continuous spectrum. The inventors recognized that parameters such as the thickness and thickness change values ​​of the first and second dielectric layers may be selected to provide the desired transmittance change behavior only at the first, second, and third wavelengths, and that the layers may not need to provide the same transmittance behavior at other wavelengths. The inventors discovered that by limiting the transmittance change behavior to only specific wavelengths, a coating including multiple layers with the same thickness change rate can provide the desired transmittance behavior, as described above, that can be manufactured inexpensively, quickly, and reliably while providing acceptable transmission characteristics.

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

[0049] Preferably, the transmittance T(n) of the first surface at each emission point satisfies the following formula: T(n)=(T(n-1)) / ([1-T(n-1)]×[1-L]), where L is the optical loss coefficient 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 silicon, titanium, tantalum, or hafnium.

[0051] The thickness of each layer ranges from 2 to 300 nm. The thickness of each layer does not fall outside this range at any point between the first end and the second end. In some embodiments, the thickness of each layer ranges from 20 to 300 nm.

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

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

[0054] Each of the plurality of discrete values ​​of the thickness variation rate may range from −150% to +150%.

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

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

[0057] This optimization improves the performance of graded coatings by adjusting the thickness of multiple layers without changing the gradient (mask). It allows for a wider tolerance in the actual thickness gradient (both linearity and amplitude) and a wider tolerance in the mask shape. This reduces the number of mask iterations, shortening process development and prototyping time. This method also allows for correcting residual mask variations over time, especially in high-volume manufacturing, to continuously maintain yield with an automated feedback process.

[0058] In other words, disclosed herein is a method for designing or manufacturing a transmission coating for a waveguide. The transmission coating includes a plurality of layers. The method includes selecting, for each layer, (first) coating parameters and (first) coating functions from a plurality of acceptable coating functions to optimize transmission for a plurality of different wavelengths at a plurality of locations along the waveguide. The method includes forming the plurality of layers using the determined coating parameters and coating functions. The method further includes measuring a thickness of the first layer at a plurality of locations, the measurements indicating that the coating function deviates from that selected during optimization. The method is characterized by selecting different (second) coating parameters 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 reality, it is very difficult and time-consuming to precisely align the mask with the designed gradient. In mass production, the gradient may also change from time to time as the mask deteriorates. This disclosure outlines an optimization method that helps correct residual gradient variations and improve the yield and optical performance of gradient coatings. More specifically, this specification describes a method for designing a multilayer achromatic gradient transmission coating using four linear gradients. Each gradient is translated into a fixed geometric shape of a single dielectric material mask. During the coating process, the gradient mask physically blocks portions of the material from being deposited on the substrate, creating a gradient layer thickness for this material. By carefully combining multiple gradients, multiple materials, and multiple layers, the optimized coating structure can meet the spatially gradient transmission requirements of RGB windows.

[0060] Traditionally, coating thickness is measured in situ or after coating to verify coating parameters, particularly thickness profiles. If the measurements indicate that the coating mask no longer provides the desired performance, the coating mask is replaced. Therefore, this is a binary pass / fail test, and it is recognized in the art that coating masks degrade over time and require replacement (i.e., periodically "fail"). In industrial or mass-production applications, the process of stopping the production line, replacing the coating mask, and then restarting the manufacturing process is costly in terms of time and money. The inventors have recognized that additional tolerances can be achieved by using pass / fail thickness verification measurements to determine the "actual" coating function of the mask. Generally, the disclosed method involves identifying, for each layer, the coating function (a characteristic or parameter of the physical coating mask) and the coating parameters (such as user-selected parameters such as coating speed). The inventors have realized that additional tolerances for the mask's performance (i.e., changes to the specified coating function) can be achieved by using 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 of the openings in the shadow mask mentioned above). This wear can lead to inaccurate application of the layer, resulting in optical properties that differ from those desired. Step a establishes an initial set of values ​​that, under ideal conditions (i.e., no wear of the layer application / coating equipment), will produce an optimized transmittance along the entire length (and, optionally, width) of the waveguide. These values ​​can be generated by simulation, experimental trials, or other suitable methods known to those skilled in the art. This is referred to as the first optimization.

[0061] These layers are then deposited in step b. This can be done using the method described above. If there is no wear on the application equipment, there is no need to continue with this method, which is not the case in a real-world scenario. This is verified in step c by comparing the thickness of the generated layer 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 mask-specified / predicted coating function. In other words, the thickness of one (or each) layer is measured at multiple locations, and a second (measured) coating function is determined that deviates from the first (predicted) coating function. A second optimization is then performed, and second coating parameters are identified. In other words, the second coating parameters are new or updated versions of the first coating parameters after the re-optimization (or second optimization) has been performed.

[0063] In particular, the inventors realized that a certain degree of imperfection in the shadow mask can be tolerated by performing a second optimization using the coating function determined by measurement (i.e., a pass / fail test) and adjusting selected coating parameters (e.g., coating speed). That is, the inventors unexpectedly discovered that the degrees of freedom associated with the coating parameters (e.g., coating speed) can compensate for imperfections in the coating function (e.g., mask slope). Traditionally, if a mask is found to provide suboptimal performance, it is replaced. However, the inventors realized that a certain degree of suboptimal performance can be tolerated by utilizing the degrees of freedom associated with the coating parameters and performing a second (fine-tuning) optimization using the measured coating function. This approach significantly improves efficiency and extends the mask's lifespan. In other words, the inventors unexpectedly discovered that this method can produce uniform and stable coating performance even for shadow masks that have significantly deviated from their original specifications due to use.

[0064] This method can be further expanded to create an iterative re-optimization loop. In this case, there is a further step e, forming or simulating multiple layers using the deviated coating function and adjusted coating parameters of step d. Next, there is step f, determining or simulating the transmittance at multiple locations along the waveguide for multiple different wavelengths. Next, there is step g, repeating steps c through f until the transmittance determined / simulated in step f is within an acceptable tolerance of the optimized transmittance of step a. The transmittance of the generated waveguide is measured in step f. This is to close the loop established in step g with steps c through f when a waveguide with a sufficiently optimized transmittance is generated or simulated. As will be appreciated by those skilled in the art, the tolerance can be a number of different factors, such as each location having a transmittance within a set percentage error from the optimized transmittance of step a, or analyzing a plot of the transmittance along the length of the waveguide compared to the optimized transmittance curve of step a.

[0065] Each coating function may be the rate of change of layer thickness along the length of the waveguide from the first end of the waveguide to the second end of the waveguide. The number of acceptable coating functions may be 2 to 6, optionally 2 to 4, optionally 4. Each determined coating function may be linear. The measurements in step c may indicate that the coating function is nonlinear. The layer thickness measurements in step c may be achieved by curve-fitting measurements of light interacting with the layer to the expected behavior of light at different thicknesses, thereby determining the layer thickness. The light measurements may be made from light reflected by the layer or may use an ellipsometer.

[0066] By maintaining a constant number of acceptable coating functions, each layer can be applied with a single application tool (the shadow mask mentioned above), eliminating the need for tool changes, thereby improving the efficiency of the system and method.

[0067] The first coating parameter may relate to the thickness of the layer at its thinnest point. The forming of the multiple layers in step b may include controlling a flow of coating material toward the waveguide using a shadow mask. The first coating parameter may be either a rate of flow of coating material toward the waveguide or a rate at which the waveguide moves through the flow of coating material. Step a further includes determining a third coating parameter, and step d further includes determining a fourth coating parameter, the third and fourth coating parameters being either the rate of flow of coating material toward the waveguide or the 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 re-optimization (or second optimization) has been performed.

[0068] The inventors discovered that by adjusting the "base thickness" of the waveguide coating, the transmittance of each layer can be changed, and that wear on the coating equipment can cause inaccuracies in the coating function of each layer. Using these two parameters, the "base thickness" can be changed without changing the deposition equipment.

[0069] The plurality of layers may include at least one dielectric. The forming of the plurality of layers in step b may include forming alternating layers of a first material and a second material. The first material is a first dielectric, and the second material is 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 previously mentioned, these materials have various 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 positions along the waveguide satisfies the following equation: T(n)=(T(n-1)) / ([1-T(n-1)]×[1-L]), where L is the optical loss coefficient of the waveguide material.

[0072] These follow the optimum properties of the waveguide explained above.

[0073] The optimization of steps a and e may include further considering the transmittance of an additional transmitting coating on the surface opposite to that on which the transmitting coating is deposited.

[0074] In this way, the deposited coating can be adjusted to account for inaccuracies in the transmittance of the opposing coated surface acting in parallel, or the deposited coating can be adjusted to favor or disadvantage certain wavelengths of light, to correct for the optical properties of the system or to create a particular visual effect for the user.

[0075] The deviating coating function may be determined by fitting the original coating function to the measured film thickness, allowing 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 coating parameters for each layer at each of a plurality of locations.

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

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

[0079] According to a fourth aspect, there is provided a holographic system including a display device configured to display a hologram of an image and to output light spatially modulated in accordance with the hologram, and the first waveguide as described above. The holographic system may further include a second waveguide.

[0080] According to a fifth aspect, there is provided a method for depositing a transmission coating on a waveguide. The transmission coating includes multiple layers. The method includes step a) of determining first coating parameters and selecting a coating function for each layer to optimize transmission for multiple different wavelengths at multiple locations along the waveguide. The coating function is selected from a multiple of acceptable coating functions, such as four acceptable coating functions. Next, step b) is forming the first layer using the determined coating parameters and coating function. Next, step c) is identifying deviations in the coating function from those determined during optimization of step a) by measuring the thickness of at least the first layer at each of the multiple locations. Thereafter, step d) is repeating the optimization of transmission for multiple different wavelengths at multiple locations along the waveguide by adjusting the coating parameters of a second layer using the measured coating function for each layer. Finally, step e) is repeating steps b through d for the second layer, followed by step e for each subsequent layer.

[0081] This method is similar to the method of the first embodiment, but in this method, adjustments are made after each layer is formed, and the adjustments take into account inaccuracies that occurred in the formation of the previous layer. This produces a more optimal coating in one set of layer deposition (i.e., no need to repeat a suboptimal coating multiple times), but produces a less optimal coating compared to the final version produced according to the method of the first embodiment, at least because the layers, when viewed holistically, can better optimize the transmittance over the length of the waveguide.

[0082] The term "hologram" refers to a recording containing amplitude or phase information about an object, or a combination thereof. The term "holographic reconstruction" refers to an 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 spatially separated from the hologram. The term "replay field" refers to the 2D region in which the holographic reconstruction is formed and perfectly focused. When a hologram is displayed on a spatial light modulator containing pixels, the replay field is repeated in multiple diffraction orders, each of which is a replica of the zeroth-order replay field. The zeroth-order replay field is the brightest replay field and therefore generally corresponds to the dominant or primary replay field. Unless explicitly stated otherwise, the term "replay field" is interpreted as referring to the zeroth-order replay field. The term "replay plane" refers to the plane in space containing all replay fields. The terms "image," "replayed image," and "image region" refer to the region of the replay field illuminated by the light of the holographic reconstruction. In some embodiments, an "image" is made up of individual spots called "image spots" or, for convenience, "image pixels."

[0083] The terms "encoding," "writing," or "addressing" are used to describe the process of providing a plurality of pixels of an SLM with a plurality of control values ​​that respectively determine the modulation level of each pixel. The pixels of the SLM are said to be configured to "display" a light modulation distribution in response to receiving the plurality of control values. The SLM is therefore said to "display" a hologram, and a hologram can be thought of as an array of light modulation values ​​or levels.

[0084] It has been shown 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 are sometimes referred to as phase-only holograms. Although the embodiments relate to phase-only holograms, the present disclosure is equally applicable to amplitude-only holography.

[0085] The present disclosure is equally 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 complex modulation using a so-called full complex hologram, which contains both amplitude and phase information associated with the original object. Such holograms are sometimes referred to as full complex holograms because the value (gray level) assigned to each pixel of the hologram has an amplitude and a phase component. The value (gray level) assigned to each pixel can be represented as a complex number having both an amplitude and a phase component. In some embodiments, a full complex computer-generated hologram is calculated.

[0086] The phase of a pixel in a computer-generated hologram or spatial light modulator, referred to as a phase value, phase component, phase information, or simply phase, is sometimes referred to as an abbreviation for "phase delay." That is, the described phase value is actually a numerical value (e.g., ranging from 0 to 2π) that represents the amount of phase delay provided by that pixel. For example, a spatial light modulator pixel described as having a phase value of π / 2 delays the phase of received light by π / 2 radians. In some embodiments, each pixel in a spatial light modulator is operable at one of multiple possible modulation values ​​(e.g., phase delay values). The term "gray level" is sometimes used to refer to multiple available modulation levels. For example, the term "gray level" is sometimes used for convenience to refer to multiple phase levels available in a phase-only modulator, even though the different phase levels do not provide different shades of gray. The term "gray level" is sometimes used for convenience to refer to multiple complex modulation levels available in a complex modulator.

[0087] A hologram therefore consists of an array of gray levels, i.e., an array of optical modulation values, such as an array of phase delay values ​​or complex modulation values. A hologram can also be considered a diffraction pattern, since it is a pattern displayed on a spatial light modulator and causes diffraction when illuminated with light of a wavelength comparable to (but usually shorter than) the pixel pitch of the spatial light modulator. Here, we refer to combining holograms with other diffraction patterns, such as diffraction patterns that function as lenses or gratings. For example, a diffraction pattern that functions as a grating can be combined with a hologram to transform the replay field onto the reconstruction plane, or a diffraction pattern that functions as a lens can be combined with a hologram to focus the holographic reconstruction onto the reconstruction plane in the near field.

[0088] In the detailed description that follows, different embodiments and groups of embodiments may be disclosed separately, but 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, i.e., all possible combinations and permutations of features disclosed in this disclosure are contemplated. [Brief explanation of the drawings]

[0089] Specific embodiments will now be described, by way of example only, with reference to the following figures: [Figure 1] FIG. 1 is a schematic diagram showing a reflective SLM generating a holographic reconstruction on a screen. [Figure 2A] The first iteration of an example Gerchberg-Saxton type algorithm is shown. [Figure 2B] The second and subsequent iterations of an example Gerchberg-Saxton type algorithm are shown. [Figure 2C] 1 illustrates the second and subsequent alternative iterations of an example Gerchberg-Saxton type algorithm. [Figure 3] 1 is a schematic diagram of a reflective LCO S SLM. [Figure 4A] Shown is an image (bottom) containing multiple image regions and a corresponding hologram (top) containing multiple hologram components. [Figure 4B] 1 illustrates a hologram characterized by routing or channeling holographically encoded light into multiple individual holographic channels. [Figure 5] FIG. 4B shows a system arranged to direct the optical content of each hologram channel to the eye along a different optical path. [Figure 6] FIG. 1 shows a perspective view of a pair of stacked image replicators arranged to expand a beam in two dimensions. [Figure 7] 1 shows a cross-sectional schematic diagram of a first waveguide according to the present disclosure. [Figure 8] 8 shows an enlarged schematic cross-sectional view of a portion of the first waveguide of FIG. 7. [Figure 9] 1 is a graph showing the increase in ideal transmittance of a waveguide in the guiding direction. [Figure 10] 10A and 10B show graphs for a first example waveguide according to the present disclosure including 12 alternating layers of SiO2 and TiO2, where FIGS. 10A and 10B show the thicknesses of the SiO2 and TiO2 layers, respectively, and FIG. 10C shows the transmittance of a first face of the first example waveguide compared to the ideal transmittance at the red, green, and blue wavelengths for which the waveguide is designed. [Figure 11] 10 shows a graph comparing the transmittance of the waveguide of the first embodiment with the ideal transmittance at other wavelengths. [Figure 12] 1 is a cross-sectional schematic diagram illustrating a portion of an apparatus for fabricating waveguides according to the present disclosure, with a waveguide substrate passing under a source of dielectric material. [Figure 13] 13 is a schematic diagram of a shadow mask of the device of FIG. 12 with four openings, the cross section of which is in a plane perpendicular to the plane of the cross section of FIG. 12; [Figure 14] 14A, 14B, 14C, and 14D show cross-sectional schematic views of four different waveguide substrates each having a layer of dielectric material formed on a first surface using the mask of FIG. 13, with each layer being formed using a different opening in the mask. [Figure 15] 1 illustrates a first method of applying a transmission coating to a waveguide according to the present disclosure. [Figure 16] 1 shows an expanded version of a first method for applying a transmission coating to a waveguide according to the present disclosure. [Figure 17] 1 illustrates a second method for applying a transmission coating to a waveguide according to the present disclosure. [Figure 18] 18A and 18B show graphs of an example of a simulated optimized transmission coating for a waveguide according to the present disclosure, the waveguide being composed of 12 alternating layers of first and second dielectric materials, where FIGS. 18A and 18B show the thicknesses of the first and second dielectric material layers, respectively, and FIG. 18C shows the transmittance of the simulated optimized transmission coating compared to the ideal transmittance at the red, green, and blue wavelengths for which the transmission coating was designed. [Figure 19] 19A and 19B show graphs for a first example of a transmission coating for a waveguide deposited by a method according to the present disclosure, the waveguide being composed of 12 alternating layers of first and second dielectric materials, where FIGS. 19A and 19B show the thicknesses of the first and second dielectric material layers, respectively, and FIG. 19C shows the transmittance of the transmission coating compared to the ideal transmittance at the red, green, and blue wavelengths for which the transmission coating was designed. The same reference numbers are used throughout the drawings to refer to the same or similar parts. DETAILED DESCRIPTION OF THE INVENTION

[0090] The present invention is not limited to the embodiments described below, but rather encompasses the full scope of the appended claims, i.e., the present invention may be embodied in different forms and should not be construed as being limited to the embodiments set forth for illustrative purposes.

[0091] Singular terms may include plurals unless otherwise specified.

[0092] A structure described as being formed on top / bottom of, or above / below, another structure is to be interpreted as including cases where the structures contact each other and even cases where a third structure is disposed between them.

[0093] When describing temporal relationships, for example, when the temporal order of events is described as "after," "succeeding," "next," "before," etc., the disclosure should be construed as including sequential and non-sequential events unless otherwise specified. For example, unless words such as "just," "immediately," "directly," etc. are used, the description should be construed as including non-sequential cases.

[0094] In this specification, terms such as "first" and "second" may be used to describe various elements, but these elements are not limited by these terms. These terms are used only to distinguish one element from another. For example, a first element could be referred to as a second element, and similarly, a second element could be referred to as a first element, without departing from the scope of the appended claims.

[0095] Features of different embodiments may be partially or wholly combined or combined with one another and may interoperate with one another in various ways, and some embodiments may execute independently of one another or may execute together in an interdependent manner.

[0096] optical configuration FIG. 1 illustrates an embodiment in which a computer-generated hologram is encoded onto a single spatial light modulator. The computer-generated hologram is the Fourier transform of the object for reconstruction. Therefore, the hologram can be said to be a Fourier-domain, frequency-domain, 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 onto the spatial light modulator, and a holographic reconstruction is formed at a replay field, e.g., a light-receiving surface such as a screen or diffuser.

[0097] A light source 110, e.g., a laser or laser diode, is positioned to illuminate the SLM 140 through a collimating lens 111. The collimating lens directs a nearly planar wavefront of light into the SLM. In FIG. 1, the wavefront direction is not perpendicular (e.g., 2 or 3 degrees away from true perpendicular to the plane of the transparent layer). However, in other embodiments, a nearly planar wavefront is provided at normal incidence, and a beam splitter arrangement is used to separate the input and output optical paths. In the embodiment shown in FIG. 1, light from the light source is arranged to reflect off the mirrored back surface of the SLM and interact with the light modulating layer to form an output wavefront 112. The output wavefront 112 is applied to an optical system including a Fourier transform lens 120 focused onto a screen 125. More specifically, the Fourier transform lens 120 receives the modulated beam of light from the SLM 140 and performs a frequency-space transformation to generate a holographic reconstruction on the screen 125.

[0098] Notably, in this type of holography, each pixel of the hologram contributes to the overall reconstruction: there is no one-to-one correlation between a specific point on the replay field (or image pixel) and a specific light-modulating element (or hologram pixel). In other words, the modulated light leaving the light-modulating layer is distributed throughout the entire replay field.

[0099] In these embodiments, the position of the holographic reconstruction in space is determined by the refractive power (focusing power) of the Fourier transform lens. In the embodiment shown in FIG. 1, the Fourier transform lens is a physical lens. That is, the Fourier transform lens is an optical Fourier transform lens, and the Fourier transform is performed optically. Any lens can function as a Fourier transform lens, but the performance of the lens limits the accuracy of the Fourier transform that is performed. A skilled technician understands how to use lenses to perform an optical Fourier transform.

[0100] Hologram Calculation In some embodiments, the computer-generated hologram is a Fourier transform hologram, or simply a Fourier hologram, or a Fourier-based hologram, which utilizes the Fourier transform properties of a positive lens to reconstruct an image in the far field. A Fourier hologram is calculated by Fourier transforming the desired light field at the reconstruction plane back to the lens plane. A computer-generated Fourier hologram can be calculated using the Fourier transform.

[0101] Fourier transform holograms can be calculated using algorithms such as the Gerchberg-Saxton algorithm. Furthermore, the Gerchberg-Saxton algorithm can be used to calculate holograms in the Fourier domain (i.e., Fourier transform holograms) from amplitude-only information in the spatial domain (e.g., a photograph). The phase information associated with the object is effectively "obtained" from the 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 variations thereof.

[0102] The Gerchberg-Saxton algorithm considers the situation where the intensity cross sections of a light ray, IA(x,y) and IB(x,y), are known in planes A and B, respectively, and IA(x,y) and IB(x,y) are related by a single Fourier transform. Given the intensity cross sections, approximations of the phase distributions, ΨA(x,y) and ΨB(x,y), in planes A and B, respectively, are found. The Gerchberg-Saxton algorithm follows an iterative process to find a solution to this problem. Specifically, the Gerchberg-Saxton algorithm repeatedly transfers data sets (amplitude and phase) representing IA(x,y) and IB(x,y) between the spatial and Fourier (spectral or frequency) domains, while iteratively applying spatial and spectral constraints. 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 configured to generate a hologram representing the input image. The hologram can be either an amplitude-only hologram, a phase-only hologram, or a fully complex hologram.

[0103] In some embodiments, phase-only holograms are calculated using an algorithm based on the Gerchberg-Saxton algorithm, such as that described in British Patent Nos. 2,498,170 or 2,501,112, which are incorporated herein by reference in their entireties. However, the embodiments disclosed herein describe the calculation of phase-only holograms by way of example only. In these embodiments, the Gerchberg-Saxton algorithm takes phase information Ψ[u,v] of a Fourier transform of a data set and generates known amplitude information T[x,y]. The amplitude information T[x,y] represents a target image (e.g., a photograph). Because the Fourier transform inherently combines amplitude and phase, the transformed amplitude and phase contain useful information about the accuracy of the calculated data set. Therefore, the algorithm can be used iteratively using feedback on both the amplitude and phase information. However, in these embodiments, only the phase information Ψ[u,v] is used as the hologram to form a holographic representation of the target image in the image plane. The hologram is a data set (e.g., a 2D array) of phase values.

[0104] In another embodiment, an algorithm based on the Gerchberg-Saxton algorithm is used to calculate a full complex hologram, which is a hologram that has an amplitude and a phase component. A hologram is a data set (e.g., a 2D array) that contains an array of complex data values, each of which consists of an amplitude and a phase component.

[0105] In some embodiments, the algorithm processes complex data and the Fourier transform is a complex Fourier transform. The complex data can be considered to include (i) a real component and an imaginary component, or (ii) a magnitude component and a phase component. In some embodiments, the two components of the complex data are processed differently at various stages of the algorithm.

[0106] FIG. 2A illustrates the first iteration of an algorithm according to some embodiments for computing a phase-only hologram. The input to the algorithm is an input image 210, which includes a 2D array of pixels or data values, each of which is a magnitude or amplitude value. That is, each pixel or data value in the input image 210 lacks a phase component. Therefore, the input image 210 can be viewed as a magnitude-only, amplitude-only, or intensity-only distribution. Examples of such an input image 210 include a photograph or a single frame of a video containing a time sequence of frames. The first iteration of the algorithm begins with a data formation step 202A, in which a random phase distribution (or random phase seed) 230 is used to assign a random phase value to each pixel of the input image to form an initial composite dataset. Each data element in this dataset contains a magnitude and a phase. The initial composite dataset can be said to represent the input image in the spatial domain.

[0107] First processing block 250 receives the starting 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 the phase levels that can be represented on a pixel of a spatial light modulator 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 containing an array of complex data values ​​(each including an amplitude and 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 allowable complex modulation levels to form hologram 280A. The constraining step includes setting each complex data value to the nearest allowable complex modulation level in the complex plane. Hologram 280A can be said to represent the input image in the spectral domain, the Fourier domain, or the frequency domain. In some embodiments, the algorithm stops at this point.

[0108] However, in other embodiments, the algorithm continues as indicated by the dotted arrow in Figure 2A. In other words, the steps following the dotted arrow in Figure 2A are optional (i.e., not required for all embodiments).

[0109] A 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, which is said to represent the input image in the spatial domain.

[0110] The fourth processing block 259 receives the inverse Fourier transformed complex data set and extracts a magnitude value distribution 211A and a phase value distribution 213A. Optionally, the fourth processing block 259 evaluates the magnitude value distribution 211A. Specifically, the fourth processing block 259 compares the magnitude value distribution 211A of the inverse Fourier transformed complex data set with the input image 510, which is itself a magnitude value distribution. If the difference between the magnitude value distribution 211A and the input image 210 is sufficiently small, the fourth processing block 259 can determine that the hologram 280A is acceptable. That is, if the difference between the magnitude value distribution 211A and the input image 210 is sufficiently small, the fourth processing block 259 determines that the hologram 280A is a sufficiently accurate representation of the input image 210. In some embodiments, the phase value distribution 213A of the inverse Fourier transformed complex data set is ignored for purposes of comparison. It will be understood that any number of different methods for comparing magnitude value distribution 211A with input image 210 may be employed, and the present disclosure is not limited to any particular method. In some embodiments, a mean squared difference is calculated, and if the mean squared difference is less than a threshold, hologram 280A is deemed acceptable. If fourth processing block 259 determines that hologram 280A is not acceptable, further iterations of the algorithm are 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.

[0111] 2B depicts the second iteration of the algorithm and subsequent 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 formation step 202A combined the distribution of amplitude values ​​of the input image 210 with the random phase distribution 230 to form an initial composite data set. However, in the second and subsequent iterations, the data formation step 202B includes combining (i) the distribution of phase values ​​213A from the previous iteration of the algorithm and (ii) the distribution of amplitude values ​​of the input image 210 to form a composite data set.

[0112] The complex data set formed by data formation step 202B of FIG. 2B is processed in the same manner as described with reference to FIG. 2A to form second iteration hologram 280B. Therefore, the process description will not be repeated here. The algorithm stops once second iteration hologram 280B has been calculated. However, any number of further iterations of the algorithm can be performed. It will be appreciated that third processing block 256 is only necessary if fourth processing block 259 or further iterations are required. The output hologram 280B will generally improve with each iteration. However, in practice, a point will typically be reached where no measurable improvement is observed or the positive benefits of performing further iterations are outweighed by the negative impact of additional processing time. Therefore, the algorithm is described as iterative and convergent.

[0113] 2C depicts an alternative embodiment for the second or subsequent iteration. The distribution of phase values ​​213A from the previous iteration is fed back through the processing blocks of the algorithm. The distribution of magnitude values ​​211A is replaced with an alternative distribution of magnitude values. In this alternative embodiment, the alternative distribution of magnitude values ​​is derived from the distribution of magnitude values ​​211 from the previous iteration. Specifically, processing block 258 subtracts the distribution of magnitude values ​​of input image 210 from the distribution of magnitude values ​​211 from the previous iteration, scales the difference by a gain factor α, and subtracts the scaled difference from input image 210. This is expressed mathematically as follows, where the subscript and number indicate the iteration number:

number

[0114] 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 a function of the number of iterations only.

[0115] The embodiment of Figure 2C is in all other respects identical to the embodiments of Figures 2A and 2B. A phase-only hologram Ψ(u,v) can be said to contain a phase distribution in the frequency domain or Fourier domain.

[0116] In some embodiments, the Fourier transform is performed using a spatial light modulator. Specifically, the hologram data is combined with second data that provides optical power. That is, the data written to the spatial light modulator 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 emulates a physical lens; that is, it focuses light in the same way as a corresponding physical optical system. Thus, the lens data provides optical power, or focusing power. In these embodiments, the physical Fourier transform lens 120 in FIG. 1 can be omitted. Methods for calculating the data representing a lens are known. The data representing a lens is sometimes referred to as a software lens. For example, a phase-only lens can be created by calculating the phase delay that occurs at each point in the lens due to the lens's refractive index and the spatially varying optical path length. For example, the optical path length at the center of a convex lens is longer than the optical path length at the edge of the lens. An amplitude-only lens can be created using a Fresnel zone plate. Also known in the field of computer-generated holography are methods for combining data representing lenses with a hologram, thereby allowing the Fourier transform of the hologram to be performed without the need for a physical Fourier lens. In some embodiments, the lens data is combined with the hologram through simple addition, such as simple vector addition. In some embodiments, a physical lens is used in combination with a software lens to perform the Fourier transform. Alternatively, in other embodiments, the Fourier transform lens is omitted entirely, and the holographic reconstruction is performed in the far field. In further embodiments, the hologram may also be combined with grating data, i.e., data configured to perform the function of a grating, such as image steering. Again, methods for calculating such data are known in the art. For example, a phase-only grating may be formed by modeling the phase delay caused by each point on the surface of a blazed grating. An amplitude-only grating can be simply superimposed with an amplitude-only hologram to provide angular steering of the holographic reconstruction.The second data that provides the lens effect and / or steering is sometimes called a light processing function or a light processing pattern to distinguish it from the hologram data, which is sometimes called an image forming function or an image forming pattern.

[0117] In some embodiments, the Fourier transform is performed jointly by a physical Fourier transform lens and a software lens, i.e., some of the optical power contributing to the Fourier transform is provided by the software lens, and the remaining optical power contributing to the Fourier transform is provided by the physical optics.

[0118] In some embodiments, a real-time engine is provided that is configured to receive image data and use an algorithm to calculate a hologram in real time. In some embodiments, the image data is a video that includes a series of image frames. In other embodiments, the hologram is pre-calculated, stored in computer memory, and recalled for display on the SLM as needed. That is, in some embodiments, a repository of pre-defined holograms is provided.

[0119] The embodiments relate, by way of example, to Fourier holography and Gerchberg-Saxton type algorithms. The present disclosure is equally applicable to Fresnel holography and Fresnel holograms, which can be calculated in a similar manner. The present disclosure is also applicable to holograms calculated with other techniques, such as those based on point cloud methods.

[0120] Light Modulation Spatial light modulators 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 phase is required. If the hologram is a fully compound hologram, a spatial light modulator that modulates phase and amplitude can be used, or one spatial light modulator that modulates phase and a second spatial light modulator that modulates amplitude can be used.

[0121] In some embodiments, the light modulation elements (i.e., pixels) of the spatial light modulator are cells containing 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 a plurality of light modulation levels. That is, each liquid crystal cell is configured to operate at any one light modulation level selected from a plurality of possible light modulation levels. Each liquid crystal cell is dynamically reconfigurable to a different light modulation level 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, although the present disclosure is not limited to this type of spatial light modulator.

[0122] LCOS devices offer a dense array of light-modulating elements (pixels) within a small aperture (e.g., a few centimeters wide). Because pixels are typically about 10 microns or smaller, the diffraction angle is a few degrees, allowing for compact optics. The small aperture of an LCOS LM can provide better illumination than the larger apertures of other liquid crystal devices. Because LCOS devices are typically reflective, the circuitry that drives the LCOS LM's pixels can be embedded beneath the reflective surface, resulting in a high aperture ratio. In other words, because the pixels are densely packed, there is little dead space between them. This is advantageous because it reduces optical noise in the replay field. LCOS LMs use silicon backplanes, which have the advantage that the pixels are optically flat. This is particularly important for phase-modulating devices.

[0123] A suitable LCOS LM will now be described, by way of example only, with reference to Figure 3. The LCOS device is formed using a single crystal silicon substrate 302. On the top surface of the substrate is disposed a 2D array of square planar aluminum electrodes 301 spaced apart by gaps 301a. Each electrode 301 is addressable via circuitry 302a embedded in the substrate 302. Each electrode forms a respective planar mirror. An alignment layer 303 is disposed on the electrode array, and a liquid crystal layer 304 is disposed on the alignment layer 303. A second alignment layer 305 is disposed on a planar transparent layer 306, for example of glass. Between the transparent layer 306 and the second alignment layer 305 is disposed a single transparent electrode 307, for example of ITO.

[0124] Each square electrode 301, together with the area overlying the transparent electrode 307 and the intervening liquid crystal material, defines a controllable phase-modulating element 308, often 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 space 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 in each phase-modulating element can be altered, thereby imparting a variable retardation to light incident thereon. The effect is to impart a phase-only modulation to the wavefront; no amplitude effects are produced.

[0125] The described LCOS SLMs output spatially modulated light upon reflection. An advantage of reflective LCOS SLMs is that the signal lines, gate lines, and transistors are located below the mirror surface, resulting in a high fill factor (typically 90% or higher) and high resolution. Another advantage of using reflective LCOS spatial light modulators is that the thickness of the liquid crystal layer can be half that of using transmissive devices, which significantly improves the switching speed of the liquid crystal (an important advantage for projecting moving images). However, the teachings of this disclosure can be implemented using transmissive LCOS SLMs as well.

[0126] Light Channeling The optical systems disclosed herein are applicable to pupil dilation with any diffracted light field. In some embodiments, the diffracted light field is a holographic light field, i.e., a complex 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 splits / channels image content. This type of hologram is described further herein, but merely as an example of a diffracted light field compatible with the present disclosure. Other types of holograms may also be used in combination with the viewing systems and light engines disclosed herein.

[0127] The following describes display systems and methods 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 expand the area (or interior) of light emitted by a relatively small light emitter (such as a relatively small SLM or other pixelated display device used in the configurations described herein) that can be viewed by a human viewer or other viewing system at a distance (e.g., a relatively large distance) from the light emitter. The waveguide accomplishes this by increasing the number of transmission points through which the light is output toward the observer. As a result, the light becomes visible from multiple different observer positions; for example, an observer can move their head and gaze while viewing the light from the light emitter. Thus, the use of a waveguide pupil expander can be said to expand the observer's "eyebox" or "eye motion box." This has many useful applications, including, but not limited to, head-up displays and automotive head-up displays.

[0128] The display systems described herein may be configured to direct light, such as a diffracted light field, through a waveguide pupil dilator to provide pupil dilation in at least one dimension, e.g., 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, but is not limited to, a computer-generated hologram (CGH), such as a point cloud hologram, a Fresnel hologram, or a Fourier hologram. The hologram is sometimes referred to as a "diffractive structure" or "modulation pattern." The SLM or other display device may be arranged to display a diffractive pattern (or modulation pattern) comprising the hologram and one or more other elements, such as a software lens or diffraction grating, in a manner familiar to the skilled reader.

[0129] A hologram may be calculated to provide channeling of a diffracted light field. This is described in detail in GB 2101666.2, GB 2101667.0, and GB 2112213.0, all of which are incorporated herein by reference. Generally speaking, a hologram may be calculated to correspond to an image to be holographically reconstructed. The image to which the hologram corresponds is sometimes referred to as the "input image" or "target image." A hologram may be calculated to form a light field (output by the SLM) that includes a cone of spatially modulated light when displayed on an SLM and appropriately illuminated. In some embodiments, the cone includes multiple successive optical channels of spatially modulated light corresponding to respective successive regions of the image. However, the present disclosure is not limited to this type of hologram.

[0130] Although reference is made herein to a "hologram" or a "computer-generated hologram (CGH)," it will be understood that the SLM may be configured to dynamically display multiple different holograms, either sequentially or in sequence. The systems and methods described herein are applicable to the dynamic display of multiple different holograms.

[0131] 4A-5 show an example, but not limiting, of a hologram that can be displayed on a display device such as an SLM, which can be used in combination with the pupil dilation apparatus disclosed herein.

[0132] FIG. 4A illustrates a projection image 452 containing eight image regions / components V1 through V8. Figure 4A shows eight image components by way of example only; image 452 may be divided into any number of components. Figure 4A also illustrates an encoded light pattern 454 (i.e., a hologram) from which image 452 can be reconstructed, for example, when transformed by lenses in an appropriate viewing system. Encoded light pattern 454 is composed of first through eighth sub-holograms or components H1 through H8, corresponding to the first through eighth image components / regions V1 through V8. Figure 4A further illustrates how a hologram decomposes image content by angle. Thus, a hologram is characterized by the light channeling it performs. This is illustrated in FIG. 4B. Specifically, the hologram in this example directs light into multiple discrete regions. While the discrete regions are disks in the illustrated example, other shapes are also contemplated. The optimal disk size and shape may be related to the size and shape of the observation system's entrance pupil after propagation through the waveguide.

[0133] FIG. 5 shows a viewing system 500 including a display device that displays the holograms calculated as shown in FIGS. 4A and 4B.

[0134] The viewing system 500 includes a display device, which in this arrangement includes an LCOS 502. The LCOS 502 is arranged to display a modulation pattern (or "diffraction pattern") comprising a hologram and project the holographically encoded light toward an eye 505, which includes a pupil acting as an aperture 504, a lens 509, and a retina (not shown) acting as a display surface. There is a light source (not shown) arranged to illuminate the LCOS 502. The lens 509 of the eye 505 performs the conversion of the hologram to an image. The light source may be of any suitable type, for example, it may consist of a laser light source.

[0135] Viewing system 500 further comprises a waveguide 508 disposed between LCOS 502 and eye 505. The presence of waveguide 508 allows all angular content from LCOS 502 to be received by the eye, even at the relatively long projection distances shown, because waveguide 508 acts as a pupil expander, a method that is well known and will only be described briefly here.

[0136] Briefly, the waveguide 508 shown in FIG. 5 comprises a substantially elongated structure. In this example, the waveguide 508 comprises an optical slab of refractive material, although other types of waveguides are well known and may be used. The waveguide 508 is positioned, for example, at an oblique angle, to intersect with the light cone (i.e., the diffracted light field) projected from the LCOS 502. In this example, the size, location, and position of the waveguide 508 are configured so that light from each of eight ray bundles within the light cone enters the waveguide 508 through a first planar surface of the waveguide 508 (closest to the LCOS 502) and is guided at least partially along the length of the waveguide 508 before emitting through a second planar surface (closest to the eye) substantially opposite the first surface. As will be appreciated, the second planar surface may be partially reflective and partially transmissive. In other words, as each ray of light travels within the waveguide 508 from a first plane and strikes a second plane, some of the light is transmitted out of the waveguide 508, and some is reflected off the second plane back to the first plane. The first plane is reflective, so all of the light that strikes the first plane from within the waveguide 508 is reflected off the second plane. Thus, some of the light is refracted between the two planes of the waveguide 508 before being transmitted, while other light is reflected and undergoes one or more reflections (or "bounces") between the planes of the waveguide 508 before being transmitted.

[0137] FIG. 5 illustrates a total of nine "bounce" points B0-B8 along the length of waveguide 508. As shown in FIG. 4A, light associated with all points (V1-V8) of the image is transmitted from the waveguide at each "bounce" from the second plane of waveguide 508; however, only light from one angular portion of the image (e.g., any light from V1-V8) has a trajectory that allows it to reach eye 505 from each "bounce" point B0-B8. Furthermore, light from different angular portions of the image V1-V8 reaches eye 505 from each "bounce" point. Thus, in the example of FIG. 5, each angular channel of encoded light reaches the eye only once from waveguide 508.

[0138] The above-described methods and arrangements may be implemented in a variety of applications and viewing systems, for example, in head-up displays (HUDs) and head- or helmet-mounted devices (HMDs), such as augmented reality (AR) HMDs.

[0139] Although this specification has generally discussed virtual images, in which the eye must transform received modulated light to form a perceived image, the methods and arrangements described herein can also be applied to real images.

[0140] 2D pupil dilation While the arrangement shown in Figure 5 includes a single waveguide that provides pupil dilation in one dimension, pupil dilation can be provided in more than one dimension, e.g., two dimensions. Additionally, while the example of Figure 5 uses a calculated hologram to create channels of light that correspond to different portions of an image, this disclosure and the systems described below are not limited to such types of holograms.

[0141] FIG. 6 shows a perspective view of a system 600 that includes two replicators 604, 606 arranged to expand a light beam 602 in two dimensions.

[0142] In system 600 of FIG. 6, first replicator 604 comprises a first pair of surfaces stacked parallel to one another and arranged to provide replication (or pupil dilation) similar to waveguide 508 of FIG. 5. The first pair of surfaces are similar (possibly identical) in size and shape to one another and are substantially elongated in one direction. A collimated light beam 602 is directed to the input of first replicator 604. As is well known to the skilled reader, due to the process of internal reflection between the two surfaces and partial transmission of light from each of multiple output points on one of the surfaces (the top surface as shown in FIG. 6), the light of light beam 602 is replicated in a first direction along the length of first replicator 604. Thus, a first plurality of replica light beams 608 are emitted from first replicator 604 toward second replicator 606.

[0143] The second replicator 606 comprises a second pair of surfaces stacked parallel to one another and positioned to receive each of the collimated rays of the first plurality of light rays 608 and provide replication (or pupil dilation) by expanding each of those rays in a second direction substantially perpendicular to the first direction. The first pair of surfaces are similar (possibly identical) in size and shape to one another and are substantially rectangular. The second replicator is implemented in a rectangular shape so that it has a length along a first direction to receive the first plurality of light rays 608 and a length along a second, orthogonal direction to provide replication in that second direction. Through a process of internal reflection between the two surfaces and partial transmission of light from each of a plurality of output points on one of the surfaces (the top surface as shown in FIG. 6 ), light from each ray in the first plurality of light rays 608 is replicated in the second direction. Thus, a second plurality of light beams 610 is emitted from the second replicator 606, the second plurality of light beams 610 comprising replicas of the input light beam 602 along each of the first and second directions. Thus, the second plurality of light beams 610 can be considered to comprise a two-dimensional grid or array of replica light beams.

[0144] Thus, the combination of the first and second replicators 604, 605 of Figure 6 can be said to provide a two-dimensional replicator (or a "two-dimensional pupil dilator").

[0145] Improved Waveguides As described in connection with FIG. 5, light within the waveguide 508 is reflected between the partially reflective and partially transmissive surfaces and the reflective surface of the waveguide. The light may undergo one or more reflections or bounces between the two reflective / reflect-transmissive surfaces. At each bounce point on the partially transmissive surface, the light is split: a portion of the light is emitted from the waveguide, and the remaining (usually larger) portion is reflected and continues to propagate between the two surfaces of the waveguide. This allows the partially transmissive surfaces of the waveguide to provide a plurality of n emission zones for the light guided between the first and second surfaces. After each bounce point / emission zone, the intensity of the light propagating within the waveguide decreases. In other words, the intensity of the light propagating within the waveguide decreases in the direction of the guiding.

[0146] It is desirable for the intensity of light emitted from the waveguide to be substantially the same in each of the n light-emitting zones. This can be achieved by providing an improved waveguide by applying a layered coating to the partially transmitting surface of the waveguide, which reduces the transmittance of the partially transmitting surface in the waveguiding direction, thereby reducing the intensity of the propagating light in the waveguiding direction.

[0147] FIG. 7 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. An optical field 706 (represented in FIG. 7 by a single ray) is shown propagating through the waveguide 708. The second surface 704 includes an input port positioned to receive the optical field. The first surface 702 is partially transmissive and partially reflective and includes a coating 703. The term "coating" is used herein for convenience only, and those skilled in the art will understand that a component described as a "coating" can be formed by any method, including, but not limited to, a coating process. The second surface 704 is substantially totally reflective (other than at the input). FIG. 7 illustrates the path of an optical field through the waveguide as it bounces between the first and second surfaces. Each time the light field reflects off the first surface, it splits, with a portion of the light field emitting from the first surface and a remaining portion being reflected and continuing to propagate between the first and second surfaces via reflection. Thus, a radiation zone is effectively formed at each reflection point. While six radiation zones are shown in Figure 7, those skilled in the art will appreciate that there may, of course, be more or fewer reflection and radiation zones. Figure 7 is merely illustrative.

[0148] Coating 703 is comprised of multiple alternating layers of a first dielectric and multiple alternating layers of a second dielectric. This is shown in FIG. 8. The layers of the coating are referenced herein by number, with the layer adjacent to 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 furthest from first surface 702 (on top of layer 903) is 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), with these layers alternating, with subsequent SiO2 layers (first dielectric) separated by TiO2 layers (second dielectric).

[0149] Each of the layers 901-904 varies in thickness in the waveguide direction (from left to right in FIG. 9 ), and in this embodiment, by way of example, has a linear profile. In other words, the rate of change of thickness for each layer is constant. The profile of each layer can be characterized using the rate of change of thickness. Each layer has a first end 906 and a second end 908. The rate of change of thickness is defined as the change in thickness from the first end 906 to the second end 908 divided by the thickness of the first end 906 multiplied by 100. For the first layer 901, the rate of change of thickness is 100 x (final thickness 912 - initial thickness 910) / initial thickness 910.

[0150] The rate of change of thickness of layer 903 is the same as that of layer 901. Furthermore, the rate of change of both layers 901 and 903 is positive (i.e., the layer thickness increases from the first end 906 to the second end 908). Layers 902 and 904 have different rates of change relative to each other and to layers 901 and 903. Furthermore, the rate of change of both layers 902 and 904 is negative (i.e., the layer thickness decreases from the first end 906 to the second end 908).

[0151] The inventors have discovered that by selecting an appropriate number of alternating layers of first and second dielectrics, with the layers having appropriate thicknesses and rates of change in thickness from the first end to the second end, it is possible to provide a first surface of a waveguide whose transmittance increases in the direction of waveguiding. In this way, the intensity of the optical field emitted in each emission zone (i.e., the intensity of each replica emitted in each emission zone) is substantially constant. This has the advantage of providing substantially spatially uniform light emission from the waveguide.

[0152] The idealized exponential increase in transmittance of first surface 702 is illustrated in Figure 9, which is a graph showing transmittance on the Y-axis and position along first surface 702 on the X-axis. The numbers on the X-axis represent n emission zones. Specifically, transmittance is expressed by the following equation:

number

[0153] The example shown in FIG. 8 is merely representative. FIG. 8 is not drawn to scale. Typically, coatings according to the present invention are comprised of four or more layers. Below are nine examples of layered coatings according to the present disclosure that sufficiently increase the transmittance of the first surface. Each of these examples has been determined by simulation. Those skilled in the art will understand that the present disclosure is not limited to the examples disclosed herein. For example, a coating may be comprised of a different number of layers (more or fewer) than the coatings disclosed herein. Additionally, layers of different dielectric materials may be used.

[0154] Waveguide example 10a to 10c relate to a first example of a coating of the present invention. This first example coating is composed of 12 alternating layers of SiO2 and TiO2. The layers are numbered 1 through 12, and light emitted from the waveguide passes through each layer in turn. The odd-numbered layers (layers L1, L3, L5, L7, L9, and L11) are layers of SiO2. The even-numbered layers (layers L2, L4, L6, L8, L10, and L12) are layers of TiO2.

[0155] Figures 10a and 10b show how the thickness of each layer varies with distance along the first face 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 in the waveguiding direction. The numbers 1 to 10 on the X-axis represent the light-emitting zones on the first face. Figure 10a shows the SiO2 layers (i.e., the odd-numbered layers in this example). Figure 10b shows the TiO2 layers (i.e., the even-numbered layers in this example).

[0156] As shown in Figure 10a, there are two subsets of SiO2 layers. The first subset of layers has a first value of thickness change rate. These layers are represented by solid lines (i.e., unbroken lines) in Figure 10a. The second subset of layers has a second value of thickness change rate that is different from the first value. These layers are represented by dashed lines (i.e., broken lines) in Figure 10a. In this example, both the first and second values ​​are negative. In this example, the first value of change rate is -50% + / - 10%. The second value of change rate is -60% + / - 10%. To avoid misunderstanding, the first value is different from the second value. The minimum thickness of the thinnest layer is 50 nm + / - 15 nm.

[0157] As shown in Figure 10b, there are two subsets of TiO2 layers. The first subset of layers has a third value of thickness change rate. These layers are represented by the solid lines in Figure 10b. The second subset of layers has a fourth value of thickness change rate that is different from the first value. These layers are represented by the dashed lines in Figure 10b. In this example, both the first and second values ​​are positive. In this example, the third value of change rate is 20% + / - 10%. The fourth value of change rate is 60% + / - 10%. The minimum thickness of the thinnest layer is 50 nm + / - 15 nm.

[0158] Those skilled in the art will understand that two layers may have the same thickness change rate, but different maximum and minimum thicknesses. For example, a first layer with a minimum thickness of 2 nm and a maximum thickness of 4 nm would have a 100% increase. A second layer with a minimum thickness of 5 nm and a maximum thickness of 10 nm would also have a 100% increase, even though the absolute thicknesses of the two layers are different.

[0159] Coated waveguides according to the present disclosure typically perform differently at different wavelengths. As will be appreciated by those skilled in the art, a combination of blue, green, and red can be used to provide a full-color image (i.e., light having three different wavelengths). For example, many holographic systems use blue, green, and red light sources to generate full-color images. If a waveguide according to the present disclosure is suitable for use in such a system, the transmittance of the coated first surface should substantially follow the ideal transmittance shown in FIG. 9 at each desired wavelength.

[0160] FIG. 10c is a graph showing the transmittance of the first surface of the waveguide of the first example. The Y-axis represents transmittance. The X-axis represents the nth emission zone along the first surface of the waveguide. The solid line 1002 in FIG. 10c represents ideal transmission behavior (also shown in FIG. 9). The three dashed lines (broken lines) show the simulated transmittance of the waveguide at three different wavelengths of electromagnetic radiation. The three wavelengths shown in FIG. 10c are for blue 1004, green 1006, and red 1008 laser light, respectively. FIG. 10c shows how the coating of the first example provides excellent transmission performance at each of the three wavelengths.

[0161] The inventors have recognized that, when the problem of providing transmittance change behavior is limited to only three specific wavelengths, alternating layers of first and second dielectrics can achieve the desired increase in transmittance in the waveguiding direction, even when the number of distinct thickness change values ​​is less (preferably significantly less) than the total number of layers. This is advantageous because it is easier, cheaper, and more reliable to manufacture such a coating compared to a coating in which each layer has a unique thickness change. This is illustrated with respect to the first example below.

[0162] The first example is composed of 12 dielectric layers. However, the thickness change rate of each layer from the first end to the second end is one of four discrete allowable values. Specifically, the thickness change rate of each first dielectric layer is equal to either a first value or a second value, and the thickness change rate of each second dielectric layer is equal to either a third value or a fourth value. Therefore, the total number of first and second dielectric layers (i.e., 12) is greater than the total number of discrete allowable values ​​(i.e., 4). As shown in Figure 10c, the transmittance is within the allowable range at the blue, green, and red wavelengths for which the coating is designed. However, as shown in Figure 11, the transmittance of the coated waveguide does not remain within the allowable range at other wavelengths.

[0163] FIG. 11 is a graph. The Y-axis of FIG. 11 represents transmittance. The X-axis represents the nth radiation zone 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 that shown in FIG. 9 because the Y-axis scale in FIG. 11 is different from that in FIG. 9. The three dashed lines show the simulated transmittance of the waveguide at three different electromagnetic radiation wavelengths (1104, 1106, 1108) where the waveguide of the first embodiment is not configured. The three dashed lines show that the transmittance of the coated waveguide does not follow ideal behavior at each wavelength. The 1104 wavelength deviates significantly from ideal behavior.

[0164] Thus, the transmittance of a waveguide with a first embodiment coating for wavelengths other than the specific wavelengths for which the waveguide coating is designed may be unacceptable, although this is not an issue in applications where those wavelengths are not transmitted through the waveguide (i.e., are not used to form an image).

[0165] Further examples of coatings are described in GB Patent Application 2214069.3, which is incorporated herein by reference in its entirety.

[0166] Manufacturing method An advantage of the layered coatings of the present disclosure is that they can be produced in an inexpensive, fast, and reliable manner, one example of which is disclosed herein, although one skilled in the art will recognize that other methods are possible.

[0167] The method includes providing a waveguide substrate including a pair of parallel surfaces arranged to provide a waveguide therebetween, and depositing a plurality of layers of a first dielectric and a plurality of layers of a second dielectric on the waveguide substrate such that the layers of the first dielectric and the layers of the second dielectric are in an alternating configuration.

[0168] An apparatus for carrying out 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 including first through fourth trapezoidal openings, and a means for moving a waveguide substrate relative to the shadow mask. Each opening in the shadow mask is associated with a source of dielectric material. During the fabrication of each layer, the dielectric material from one of the sources is configured to flow through one of the openings in the shadow mask. The waveguide substrate is moved relative to the shadow mask (or vice versa) so that the shadow mask is between the sources and the waveguide substrate. The waveguide substrate passes under the openings, forming a layer of dielectric material on the surface of the waveguide substrate. This is shown in Figure 19.

[0169] FIG. 12 is a schematic cross-sectional view of a portion of an apparatus for fabricating a waveguide according to the present disclosure, the cross-section being in the XY plane. The portion of the apparatus shown in FIG. 12 includes a first source of SiO and a shadow mask 2004 including a first opening 2006. A waveguide substrate 2008 (in the form of a block or slab of glass or Perspex) is also shown. SiO material 2010 is configured to flow from the first source 2002 and pass through the first opening 2006 in the shadow mask 2004. The flow of material is in the negative Y direction. The shape of the first opening 2006 determines the shape of the SiO flow downstream of the shadow mask 2004. FIG. 12 is not drawn to scale.

[0170] A means (not shown) for moving the waveguide substrate 2008 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 opening 2006. In some embodiments, the movement is entirely in the X direction, although in other embodiments the waveguide substrate 2008 may be rotated in the first plane so that the movement is in both the X and Z directions.

[0171] 12, there is no dielectric coating layer on the waveguide substrate 2008 because the waveguide substrate 2008 has not yet passed under the first opening 2006. As the waveguide substrate passes under the first opening 2006 (in the X direction), a dielectric coating is deposited on the substrate. Generally, to produce a complete layer, the waveguide substrate 2008 needs to pass under the first opening 2006 multiple times until the required thickness is reached.

[0172] Once the first layer 2010 is formed, the waveguide substrate 2008 is moved under one of the sources of the second dielectric material and a second layer of the second dielectric material is formed over the first layer 2010 of the first dielectric material.

[0173] Figure 13 is a schematic diagram of a shadow mask 2004, taken in the XZ plane (i.e., orthogonal to the plane of Figure 12). The shadow mask is composed of four openings: a first opening 2006 (described above), a second opening 2102, a third opening 2104, and a fourth opening 2106. The first opening 2006 and the third opening 2104 are each connected to a source of a first dielectric material. The second opening 2102 and the fourth opening 2106 are each connected to a source of a second dielectric material. Each opening has a trapezoidal shape including a short base and a long base.

[0174] To fabricate subsequent alternating layers of first and second dielectric materials, the waveguide substrate 2008 moves sequentially under different openings. The layer order can be controlled depending on the order of the openings through which the waveguide substrate 2008 moves. To pass under different openings, the waveguide substrate 2008 is rotated / translated relative to the shadow mask 2004 so that the waveguide substrate 2008 passes under the openings in the X direction and the short and long bases of the openings are spaced apart in the Z direction. In this way, the thickness of each deposited layer in the Z direction varies. The rate of change in layer thickness from the first end to the second end (in the Z direction) depends on the rate of change in the width of the short and long bases of the respective openings. This is explained with reference to FIG. 13.

[0175] 14a-14d are cross-sectional schematic diagrams of four different first layers formed on a waveguide substrate 2008. FIG. 14a shows layer 2202 formed when the waveguide substrate 2008 passes under the first opening 2006. FIG. 14b shows layer 2204 formed when the waveguide substrate 2008 passes under the second opening 2102. FIG. 14c shows layer 2206 formed when the waveguide substrate 2008 passes under the second opening 2104. FIG. 14d shows layer 2208 formed when the waveguide substrate 12008 passes under the second opening 2106. As will be appreciated by those skilled in the art, the thickness profile of each of layers 2202-2208 corresponds to the shape of the respective opening.

[0176] In particular, layers 2202 and 2206 have a positive gradient from left to right because the widths of openings 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. Layer 2206 has a greater rate of change in thickness than layer 2202 because the rate of change in width from short base to long base of opening 2104 is greater than that of opening 2006. Layers 2204 and 2208 have a negative gradient from left to right because the widths of openings 2102 and 2106 decrease in the Z direction as the shadow mask and waveguide substrate are rotated relative to each other. Layer 2204 has a greater rate of change in thickness than layer 2208 because the rate of change in width from short base to long base of opening 2102 is greater than that of opening 2106.

[0177] As can be seen, the arrangement of the shadow mask 2004 having four differently shaped openings, two connected to a first source of dielectric material and two connected to a second source of dielectric material, provides a means for fabricating a plurality of alternating first and second dielectric layers. Each layer of the first dielectric has a thickness gradient equal to either a first value or a second value, with all layers having the first value associated with, for example, the first opening 2006, and all layers having the second value associated with, for example, the second opening 2102. Each layer of the second dielectric has a thickness gradient equal to either a first value or a second value, with all layers having a third value associated with, for example, the third opening 2104, and all layers having the second value associated with, for example, the fourth opening 2106. In other words, a means for fabricating a layered coating according to the present disclosure is provided.

[0178] An advantage of this fabrication method is that the waveguide substrate can be quickly and easily moved / rotated to pass under the openings in the shadow mask 2004 as needed to build up multiple alternating layers of first and second dielectric materials as needed. The number of unique masks with different shapes determines the number of discrete values ​​of layer thickness change available, so the thickness change rate of a particular layer can be controlled simply by selecting the order of the openings. 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.

[0179] It should be understood that the fabrication methods disclosed herein are not limited to four openings and two dielectric material sources. For example, increasing or decreasing the number of masks with different shapes simply increases or decreases the number of distinct allowable percent changes in usable layer thickness values.

[0180] Improved coating application method In summary, a further improved coating design method is provided, which method comprises: 1. Design the basic structure, which is usually a multi-layer mirror with RGB windows used at the lowest T% position. In this step, the gradient is not considered. 2. Applying a linear gradient to the multi-layer base structure and optimizing the gradient so that the coating transmittance at different positions meets all requirements; Includes:

[0181] The general idea is to use the gap between the RGB windows as a degree of design freedom to achieve a steady, synchronous increase in transmittance within the RGB windows, resulting in a design that is very sensitive to gradients, where small changes (a few percent) can significantly alter the transmittance of the coating.

[0182] In practice, the inventors discovered that it was very difficult to tune the mask to achieve the designed gradient thickness. There are several challenges: · Adjusting the mask is a time-consuming process that requires precise machining of metal. There is no simple relationship between gradient thickness and the physical gradient of the mask opening. Achieving a linear gradient thickness usually requires nonlinearity in the mask. Approaching the required gradient is usually a trial and error process, taking several iterations. In mass production, masks degrade within weeks, requiring maintenance and reconditioning, which increases the likelihood of small deviations in gradient thickness.

[0183] Typically, the gradient mask is close to the design, but not necessarily exact. To avoid these imperfect gradient masks, we describe a "post-process" coating optimization that requires no hardware modifications and can significantly improve coating performance. The method is as follows: Keep the gradient (the "coating function") fixed, i.e. accept small deviations and do not further optimize it. Find the optimal set of multilayer thicknesses that "fully exploit" a fixed gradient ("coating function").

[0184] Prior to the optimization of this disclosure, multilayer thicknesses were designed for an ideal gradient and could not be matched to the actual gradient. This optimization involves finding a set of (slightly) different thicknesses (an example of "coating parameters") that work to match the actual gradient (the measured "coating function").

[0185] FIG. 15 illustrates an improved method of applying a coating (eg, a coating described above) to a waveguide substrate 2008 using the apparatus shown in FIGS. 12-14 and described above.

[0186] First, an optimized transmittance is calculated at multiple locations along the length of the waveguide (e.g., the "bounce" points B0-B8 in FIG. 5, or the emission zones in FIGS. 7 and 10A-11). Based on this, a determination 3000 of the number of coating layers and the profile of each layer to achieve this optimized transmittance is performed (as described above), as well as a determination (also described above) of the particular shadow mask 2004, waveguide substrate 2008 velocity, and material flow rate required to apply the optimized layering. This determination 3000 outputs an optimized value 3100.

[0187] Using these optimized values ​​3100, a coating layer is deposited on the waveguide substrate 2008 in a forming step 3200, as described above, thereby forming a first coated waveguide. It is observed that the actual transmittance of the first waveguide differs from that optimized during determining 3000, taking into account factors such as wear of the shadow mask 2004. This is confirmed by measuring 3300 the layer thickness at multiple locations used in determining 3000 (any layer thickness change at any point along the waveguide will result in a transmittance change, as described above). As explained above, measuring step 3300 can use data from a pass / fail evaluation of the coating. However, the present disclosure relates to using the measurement data to determine the actual coating function of the mask, rather than simply evaluating pass / fail.

[0188] Using the values ​​of measurement 3300, the optimization completed in initial determination 3000 is repeated, accounting for differences between the simulated optimized waveguide and the waveguide actually generated in formation step 3200. In this manner, the values ​​generated by this re-optimization can be used to form a coating layer that accounts for wear and other imperfections in the shadow mask 2004 while maintaining the desired optical properties. In particular, re-optimization can exploit degrees of freedom associated with coating parameters (such as coating speed and minimum thickness) to improve performance without having to replace the mask.

[0189] In some embodiments of this method, an optimization loop can be formed, as shown in Figure 16, where repeated optimization 3400 generates a new set of values ​​3500 for the updated waveguide substrate 2008 velocity and the material flow rate required to apply the updated layer formation. Because the intended profile of each layer remains the same, there is no need to replace a worn shadow mask 2004 with a shadow mask 2004 having a different shape and / or unabraded openings.

[0190] Next, measurements 3600 of the actual transmittance of the first coated waveguide are made across points along the waveguide. This is compared to the optimized transmittance of optimized value 3100 in comparison step 3700. If this actual transmittance is within a predetermined tolerance of optimized value 3100 (i.e., within an acceptable error rate), mass production 3800 of the waveguides begins or continues (until further wear of shadow mask 2004 occurs and the process needs to be repeated). However, if the actual transmittance is not within this tolerance, a forming step 3200 forms a second coated waveguide using a new set of values ​​3500. The loop of steps 3200, 3300, 3400, and 3600 is repeated until the above tolerance is met. In this way, a set of waveguides with the required transmittance characteristics is produced, regardless of wear of shadow mask 2004, which would introduce inaccuracies into the coating deposition. For the avoidance of doubt, the present disclosure features deriving the "actual" coating function for each mask through measurements (e.g., using pass / fail test data) and using the degrees of freedom associated with the coating parameters to optimize performance and extend mask lifetime. The effectiveness of this approach is discussed below in conjunction with Figures 18-22.

[0191] FIG. 17 illustrates another method for applying a coating. First, as with the method described above, an optimized transmittance is calculated at multiple locations along the length of the waveguide (e.g., the "bounce" points B0-B8 in FIG. 5, or the emission zones in FIGS. 7 and 10A-11). From this, a determination 4000 of the number of coating layers and the profile of each layer to achieve this optimized transmittance is performed (as described above). Also performed is a determination of the specific shadow mask 2004, waveguide substrate 2008 velocity, and material flow rate required to apply the optimized layering (also described above). This determination 4000 outputs an optimized value 4100.

[0192] Using these optimized values ​​4100, a first layer of coating is deposited on the waveguide substrate 2008 in forming step 4200, as described above. As explained in connection with the method above, taking into account factors such as wear of the shadow mask 2004, it is expected that the actual transmittance of the first layer will differ from that optimized during determining 4000. This is confirmed by measuring 4300 the thickness of the first layer at multiple locations used in determining 4000 (as described above, variations in thickness lead to variations in transmittance).

[0193] Using the values ​​of measurement 4300, further optimization 4400 is completed to generate a new set of values ​​4500 related to the updated waveguide substrate 2008 velocity and material flow rate required to apply the second layer while accounting for any differences between the simulated optimized first layer and the first layer actually produced in forming step 4200. As with the method above, the intended profile of each layer remains the same, eliminating the need to replace a worn shadow mask 2004 with a shadow mask 2004 having a different shape and / or unabraded openings.

[0194] Finally, in decision step 4600, if this is the last layer to be deposited, the process ends and the coating is complete. However, if this is not the last layer, the next layer is formed in forming step 4200 using the new value set 4500. The loop of steps 4200, 4300, and 4400 is repeated until the coating is complete. In this way, even if wear of the shadow mask 2004 causes inaccuracies in the application of the coating layers, a waveguide with the required transmittance characteristics is produced.

[0195] Coating example using the improved method As an overview, Figure 18 shows a simulation of the original multilayer thickness with actual deviations in gradient thickness. Figure 18C shows that half of the gradient thicknesses (even-numbered layers) are no longer linear, and the actual gradient amplitude is also higher than the design value. The remaining half of the thicknesses (Figure 18A, odd-numbered layers) remain linear in this example. As a result, the RGB transmittance deviates from the target line 5002, as shown in Figure 18C. As an overview, in Figure 19, all gradient change rates (masks / "coating functions") remain the same, but the layer thicknesses ("coating parameters") are reoptimized. That is, the curves shift slightly up / down in the bottom-left / bottom-right plots, but the shape remains the same. After optimization, the gradient RGB transmittance is much closer to the original target. Once the optimization algorithm is complete, the optimization can be performed automatically with any gradient input (within a certain range) and return the optimal thickness in near real time.

[0196] More specifically, Figures 18a-18c relate to an actual example of a coating deposited using known methods on a shadow mask 2004 that has worn away, causing imprecision. The coating in this example is comprised of 30 alternating layers of two different dielectric materials. The layers are numbered 1-30, and light emitted from the waveguide passes through each layer in turn.

[0197] Figures 18a and 18b show how the actual measured thickness of each layer varies with distance along the first face of the waveguide (i.e., from the first end to the second end of each layer). According to this disclosure, these actual thicknesses differ from the specified thicknesses, i.e., from the designed or requested layers. This deviation may be due to mask aging. The Y-axis represents thickness, and the X-axis represents position along the waveguide. The numbers 1 through 9 on the X-axis represent the emission zones of the first face.

[0198] Coated waveguides according to the present disclosure typically perform differently at different wavelengths. As will be appreciated by those skilled in the art, a combination of blue, green, and red can be used to provide a full-color image (i.e., light having three different wavelengths). For example, many holographic systems use blue, green, and red light sources to generate full-color images. If a waveguide fabricated according to the present disclosure is suitable for use in such a system, the transmittance of the coated first surface should substantially follow the ideal transmittance shown in FIG. 9 at each desired wavelength.

[0199] FIG. 18c is a graph showing the transmittance of the first surface of the waveguide in this example. FIG. 18c can be obtained by optical measurements or simulations of the transmittance of layers L1 through L30. The Y-axis represents transmittance. The X-axis represents the nth emission zone along the first surface of the waveguide. The solid (unbroken) line 5002 in FIG. 18c represents the ideal transmission behavior (also shown in FIG. 9). The three dashed (broken) lines show the simulated transmittance of the waveguide for three different wavelengths of electromagnetic radiation. The three wavelengths shown in FIG. 18c are associated with blue 5004, green 5006, and red 5008 laser light, respectively. It can be seen that the three wavelengths 5004, 5006, and 5008 differ significantly from the ideal transmission behavior 5002 in some of the emission zones. This occurs due to imperfect performance (e.g., wear) of the shadow mask 2004, as explained above.

[0200] Figures 19a-19c show an example of the coating of Figures 18a-18c deposited according to the method of the present invention, i.e., further optimized according to the method of the present invention. This example coating includes 30 alternating layers of two different dielectric materials. The layers are numbered 1 through 30, and light emitted from the waveguide passes through each layer in turn.

[0201] 19a and 19b show how the actual measured thickness of each layer varies with distance along the first face 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 waveguiding direction. The numbers 1 through 9 on the X-axis represent the emission zones of the first face. As can be seen, the thickness of each layer L1 through L30 has shifted relative to the corresponding thickness shown in FIGS. 18a and 18b.

[0202] For the avoidance of doubt, layers L1-L30 depicted in Figures 19A and 19B have been determined using at least one coating function measured after an initial coating run and varying coating parameters during design to improve the achieved transmittance shown in Figure 19C.

[0203] FIG. 19c is a graph showing the transmittance of the first surface of the waveguide in this example. The Y-axis represents transmittance. The X-axis represents the nth emission zone along the first surface of the waveguide. The solid (unbroken) line 6002 in FIG. 19c represents the ideal transmission behavior (also shown in FIG. 9). The three dashed (broken) lines show the simulated transmittance of the waveguide for three different wavelengths of electromagnetic radiation. The three wavelengths shown in FIG. 19c are associated with blue 6004, green 6006, and red 6008 laser light, respectively. As can be seen, the tailored thicknesses of each layer L1 through L30 result in wavelengths 6004, 6006, and 6008 that are closer to the ideal transmission behavior 6002 throughout the length of the waveguide than those produced by known methods (shown in FIG. 18c). This improved transmittance was achieved without replacing or repairing a worn shadow mask 2004.

[0204] Additional Features Although the embodiments illustrate an electrically activated LCOS spatial light modulator, this is by way of example only, and the teachings of the present disclosure can similarly be implemented in any spatial light modulator capable of displaying computer-generated holograms in accordance with the present disclosure, such as any electrically activated SLM, optically activated SLM, digital micromirror device, or microelectromechanical device.

[0205] 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 diffusing surface, such as a diffusing surface or a diffusing screen. 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 that includes a display system mounted on the vehicle to provide a HUD. The vehicle may be a motor vehicle, such as a car, truck, van, lorry, motorcycle, train, airplane, boat, or ship.

[0206] The quality of the holographic reconstruction can be affected by the so-called zero-order problem, which is a consequence of the diffractive properties of the pixelated spatial light modulator. Such zero-order light is considered "noise" and includes, for example, specular reflections and other unwanted light from the SLM.

[0207] In the example of Fourier holography, this "noise" is focused at the focal point of the Fourier lens, resulting in a bright spot in the center of the holographic reconstruction. The zeroth order light can also be simply blocked, which means replacing the bright spot with a dark spot. Some embodiments include an angle-selective filter that removes only the parallel rays of the zeroth order. Embodiments also include methods for managing the zeroth order, as described in European Patent 2,030,072, which is incorporated herein by reference in its entirety.

[0208] In some embodiments, the size of the hologram (number of pixels in each direction) is equal to the size of the spatial light modulator, and the hologram fills the spatial light modulator. That is, the hologram uses all of the pixels of the spatial light modulator. In other embodiments, the hologram is smaller than the spatial light modulator. More specifically, the number of pixels of the hologram is less than the number of light-modulating pixels available in the spatial light modulator. In some of these other embodiments, a portion of the hologram (i.e., a contiguous subset of the hologram's pixels) is repeated in the unused pixels. This technique is sometimes called "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. Thus, the size of each tile is smaller than the spatial light modulator. In some embodiments, the "tiling" technique is implemented to improve image quality. Specifically, in some embodiments, the tiling technique is implemented to maximize the amount of signal content captured in the holographic reconstruction while minimizing the size of the image pixels. In some embodiments, the holographic pattern written to the spatial light modulator consists of at least one entire tile (i.e., the complete hologram) and at least one portion of a tile (i.e., a contiguous subset of pixels of the hologram).

[0209] In an embodiment, only first order replay fields are utilized and the system includes physical blocks, such as baffles, positioned to restrict the propagation of higher order replay fields through the system.

[0210] In embodiments, the holographic reconstruction is in color. In some embodiments, a technique known as spatially separated color ("SSC") is used to provide the color holographic reconstruction. In other embodiments, a technique known as frame sequential color ("FSC") is used.

[0211] The SSC method uses three spatially separated light-modulating pixel arrays for three monochromatic holograms. The advantage of the SSC method is that three holographic reconstructions can be formed simultaneously, resulting in very bright images. However, due to space limitations, when three spatially separated light-modulating pixel arrays are provided on a common SLM, only a subset of the available light-modulating pixels is used for each color, resulting in suboptimal quality for each monochromatic image. Therefore, a relatively low-resolution color image is provided.

[0212] In FSC, all pixels of a common spatial light modulator are used to sequentially display three monochromatic holograms. The monochromatic reconstructions are cycled through quickly enough that a human viewer can perceive a multicolor image from the integration of the three monochromatic images (e.g., red, green, blue, red, green, blue, etc.). The advantage of FSC is that the entire SLM is used for each color, meaning that every pixel of the SLM is used for each color image, optimizing the quality of the resulting three-color image. However, a disadvantage of FSC is that each monochromatic illumination event can only occur for one-third of the frame time, resulting in a composite color image that is approximately three times less bright than the SSC method. This drawback can potentially be addressed by overdriving the laser or using a more powerful laser, but this requires more power, increases cost, and increases the size of the system.

[0213] Although the examples describe illuminating an SLM with visible light, those skilled in the art will understand that the light source and SLM, as disclosed herein, can similarly be used to illuminate, for example, infrared or ultraviolet light. For example, those skilled in the art will be aware of techniques for converting infrared and ultraviolet light to visible light for the purpose of providing information to a user. For example, the present disclosure extends to using phosphor and / or quantum dot technology for this purpose.

[0214] In some arrangements, 2D holographic reconstructions are described as examples only. In other arrangements, the holographic reconstructions are 3D holographic reconstructions. That is, in some arrangements, each computer-generated hologram forms a 3D holographic reconstruction.

[0215] The methods and processes described herein can be implemented in a computer-readable medium. The term "computer-readable medium" includes a medium configured to store data temporarily or permanently, such as random access memory (RAM), read-only memory (ROM), buffer memory, flash memory, cache memory, etc. The term "computer-readable medium" is also intended to include any medium, or combination of media, capable of storing instructions for execution by a machine, which, when executed by one or more processors, cause the machine to perform, in whole or in part, one or more of the methods described herein.

[0216] The term "computer-readable medium" also includes cloud-based storage systems. The term "computer-readable medium" includes, but is not limited to, one or more tangible, non-transitory data repositories (e.g., data volumes) in the form of, for example, a solid-state memory chip, an optical disk, a magnetic disk, or any suitable combination thereof. In some embodiments, instructions for execution may be carried by a carrier medium. Examples of such carrier media include transitory media (e.g., a propagated signal carrying the instructions).

[0217] 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 that come within the scope of the appended claims and their equivalents.

Claims

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

2. The method of claim 1 , wherein each coating function is a rate of change of 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 of claim 2, wherein the number of acceptable coating functions is between 2 and 6, optionally between 2 and 4, optionally 4.

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

5. The method of any one of claims 1 to 4, wherein the first coating parameter relates to the thickness of the layer at its thinnest point.

6. The method of any one of claims 1 to 5, wherein forming the plurality of layers in step b comprises using a shadow mask to control the flow of coating material towards the waveguide.

7. 7. The method of claim 6, wherein the first and second coating parameters are either a velocity of the flow of the coating material toward the waveguide or a velocity at which the waveguide moves through the flow of the coating material.

8. 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 and fourth coating parameters being one of the other of a velocity of the flow of the coating material toward the waveguide or a velocity at which the waveguide moves through the flow of the coating material.

9. The method of any one of claims 1 to 8, wherein the plurality of layers comprises at least one dielectric.

10. 10. The method of any one of claims 1 to 9, wherein forming the plurality of layers in step b comprises forming alternating layers of a first material and a second material, and optionally wherein the first material is a first dielectric and the second material is a second dielectric, the first dielectric being a first oxide, fluoride, sulfide or nitrate of a first transition metal or semiconductor, the second dielectric being a second oxide, fluoride, sulfide or nitrate of a second transition metal or semiconductor, and / or wherein a difference in refractive index between the first and second materials is greater than 0.

4.

11. 11. The method of any one of claims 1 to 10, wherein the plurality of different wavelengths comprises a first wavelength, a second wavelength, and a third wavelength, and optionally, the first wavelength is in the range of 630 to 670 nm, the second wavelength is in the range of 500 to 540 nm, and the third wavelength is in the range of 430 to 470 nm.

12. The optimized transmittance T(n) at each of the plurality of locations along the waveguide is determined by the following equation: [Equation 1] 12. The method according to claim 1, wherein L is the optical loss coefficient of the waveguide material.

13. 13. The method of any one of claims 1 to 12, wherein the optimization of steps a and d further comprises taking into account the transmittance of a further transmitting coating on a surface opposite to the surface on which the transmitting coating is deposited.

14. The method of any one of claims 1 to 13, wherein the deviated coating function is determined by fitting the original coating function to the measured film thickness.

15. The method of any one of claims 1 to 14, wherein the measuring in step c comprises measuring the film thickness of each layer.

16. The method of any one of claims 1 to 15, wherein the repeated optimization of step d comprises adjusting coating parameters of each layer at each of the plurality of locations.

17. e. forming or simulating the plurality of layers using the deviated coating function and the adjusted coating parameters of step d; f. determining or simulating the transmittance at the plurality of locations along the waveguide for the plurality of different wavelengths; g. repeating steps c through f until the determined / simulated transmittance of step f is within an acceptable range of the optimized transmittance of step a; The method of any one of claims 1 to 16, further comprising:

18. A transmission coating for a waveguide formed using the method of any one of claims 1 to 17.

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

20. a display device configured to display a hologram of the image and to output light spatially modulated in accordance with said hologram; A first waveguide according to claim 19; and optionally further comprising a second waveguide.

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