Spatial Modulation Device

Abstract

A method for spatially modulating electromagnetic radiation at high frequencies is provided, where the modulation is in phase, polarization, or propagation direction, and includes a substrate carrying an array of aligned optical elements that moves relative to an incident beam of electromagnetic radiation to be modulated and measuring the relative motion. The array contains at least three optical elements and at least two different types of optical elements. At least some of the optical elements are formed from and integral with the substrate member. The optical elements may be fabricated on the substrate member by subtractive methods. The electromagnetic radiation to be modulated is incident on a region of the substrate referred to as the active region. As the substrate moves relative to the incident electromagnetic radiation, the active region also moves, changing the designations of the individual optical elements.

Description

[Technical field]

[0001] The present invention relates to a method and apparatus for spatially modulating electromagnetic radiation at high frequencies. The modulation may be in phase, polarization or propagation direction. [Background technology]

[0002] Multiplexing spectroscopy requires a means to spatially modulate the radiation field. In classical Fourier transform spectroscopy, phase modulation is performed along the optical axis by optical elements located in a plane perpendicular to the optical axis. In classical Hadamard spectroscopy, a code mask is placed in a plane intersecting the optical axis and the incident radiation is either transmitted or reflected towards a detector. In these methods, the modulation is generally along one path. Preferably, but not necessarily, the present invention can be used with High Efficiency Multiplexing (HEMX) as described in U.S. Patent Application No. 15 / 987,279, filed May 23, 2018 by the applicant (corresponding to PCT Application No. PCT / CA2018 / 050599, published November 29, 2018 as WO2018 / 213923), the disclosure of which is incorporated herein by reference. HEMS is a multiplexing method that improves the signal-to-noise ratio (SNR) of measurements of particle flux by modulating the flux along multiple paths. Therefore, HEMS methods have created a need for a new class of spatial modulators with multiple output directions, which was not required in the prior art. The present invention provides a modulation system suitable for use within a HEMS system. Although the following includes references to HEMS, it should be understood that these are by way of example only and the invention herein can be used in conjunction with other methods.

[0003] The number of spectroscopic channels of a multispectrometer is proportional to the number N of different modulation patterns applied to the input radiation of the measurement sequence. The number of spectroscopic channels can range from hundreds to thousands, depending on the spectroscopic bandwidth and resolution required by the application. In high-throughput industrial inspection applications, hundreds to thousands of objects are inspected per minute, and data for each object needs to be collected in a few milliseconds. These factors combine to require modulation speeds of over 100 kHz. Commercially available MEMS devices based on arrays of deformable micromirrors are capable of modulation duration speeds of about 5 kHz and burst mode speeds of about 50 kHz. The maximum speed is limited by the inertia of the mirror relative to the force applied to move the mirror (usually electrical). Higher speeds are possible by reducing the size of the mirror, and therefore the inertia of the mirror. However, as the size of the mirror approaches the wavelength λ of the incident radiation, the diffraction effects of the mirror edges become increasingly important. The present invention aims to reduce the edge diffraction effects by allowing larger mirrors to be used. The modulation duration speed of an array of micromirrors is limited by thermal considerations. However, MEMS devices have the desirable property of being able to dynamically change the pattern set to change resolution or focus on an area of ​​interest. Therefore, a new class of spatial modulators is needed that can operate at speeds greater than 100 kHz and that are dynamically adaptable.

[0004] Transitioning between different modulation patterns introduces undesirable convolution effects, reducing system performance. Conventionally, samples are taken at intervals where the spatial modulator configurations are close to the defined different modulation patterns. In systems that require a rapid transition between spatial modulator configurations, a significant percentage of the duty cycle is spent transitioning rather than collecting data, leading to a reduction in the achievable SNR. Therefore, a method is needed to improve the duty cycle, the number of counted photons, and the SNR. It is a further object of the present invention to improve the duty cycle by reducing the transition time. Summary of the Invention

[0005] According to one aspect of the present invention, there is provided a method for spatially modulating electromagnetic radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation onto an array of aligned optical elements on a substrate; translating the substrate to expose at least two different optical elements to the incident radiation at two different times; measuring the position of the substrate at the two different times; transmitting said location to a user; Here, the array of optical elements comprises at least three optical elements, with at least two optical elements modulating incident radiation in different ways.

[0006] According to one aspect of the present invention, there is provided a method for measuring displacement of a substrate, the method comprising: Directing a light beam onto a substrate having an array of reflective or transmissive position indicators; moving the substrate relative to the light beam so as to transmit or reflect portions of the light beam from at least two different position markers at different times; measuring the intensity of the transmitted or reflected light at a plurality of time intervals; and analyzing the measured light intensity multiple times to provide information regarding the position of the substrate.

[0007] According to one aspect of the present invention, there is provided a method for spatially modulating electromagnetic radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation onto an array of aligned optical elements on a member of a substrate; and translating the substrate member to expose at least two different optical elements to the incident radiation at two different times; Here, at least some of the optical elements are formed from and integral with the substrate member.

[0008] According to one aspect of the present invention, there is provided a method for spatially modulating electromagnetic radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation onto an array of aligned optical elements on a substrate; and translating the substrate to expose at least two different optical elements to the incident radiation at two different times; Here, the substrate is a flexible tape forming a closed loop, the tape is translated around the loop, and the optical elements are positioned along the direction of translation.

[0009] The invention includes a substrate carrying an array of aligned optical elements in relative motion with respect to an incident beam of electromagnetic radiation to be modulated, and means for measuring the relative motion, where the array contains at least three optical elements and at least two different types of optical elements. Preferably, at least some of the optical elements are formed from and are integral with the substrate member. The optical elements may be fabricated on the substrate member by a subtractive process, e.g., etching, machining, or laser cutting. The optical elements may be fabricated on the substrate member by an additive process, e.g., depositing a reflective layer.

[0010] The electromagnetic radiation to be modulated is incident on a region of the substrate referred to as the active region. All optical elements that have at least a portion of their extent in the active region are referred to as active. All remaining optical elements are referred to as inactive. As the substrate moves relative to the incident electromagnetic radiation, the active region also moves, and the designations of the individual optical elements change. Preferably, the relative motion is periodic, with each optical element falling within or outside the active region at regular intervals.

[0011] The relative motion may be translational, rotational or a combination of translational and rotational motion, provided such motion has the effect of causing the centre of the beam of electromagnetic radiation incident on the substrate to strike each optical element in a defined sequence. The choice of reference system is a matter of convenience. In this description, a reference system of incident electromagnetic radiation is used. In this case, the position of the source and direction of propagation of the incident electromagnetic radiation is fixed, and the substrate moves. The optical elements are assumed to be separated by a distance α. In the case of linear translation, the number of optical elements struck per second, referred to herein as the linear frequency, is v L = v / α, where v is the linear velocity of the substrate. For rotational motion, the number of optical elements hit per second is v L =α / rω, where ω is the angular velocity and r is the radius at which the optical elements are arranged. The dimension of the optical elements in the translational (or rotational) direction may be smaller than α, in which case there is a difference between the elements that directs the incident electromagnetic radiation in the same direction as any optical element. Preferably, the area of ​​difference, if any, is absorptive.

[0012] The arrangement for measuring the relative motion may be an optical or magnetic position encoder of conventional design, attached to the substrate. Preferably, the arrangement for measuring the relative motion is internal to the substrate. In a preferred embodiment, the substrate carries an array of reflective or transmissive position indices arranged along the translational or rotational direction of the substrate. Preferably, the array of position indices has the same periodicity as the array of optical elements. Preferably, the array of position markers is parallel and adjacent to the array of optical elements. Preferably, the position markers have a dimension α / 2. Preferably, the regions of the substrate between the position indices are coated with an absorbent material. To convey further information, the position markers may reflect or transmit different fractions of the intensity of the probe beam. For example, a first type of position marker reflecting or transmitting a first fraction of the intensity of the probe beam indicates the beginning of a sequence. A second type of position marker reflecting or transmitting a second fraction of the intensity of the probe beam indicates one of two values. A third type of position marker reflects or transmits a third fraction of the intensity of the probe beam, indicating a binary value of zero. These three types of position markers are sufficient to distinguish and label all the positions of the array. A beam of probe radiation is linearly displaced from the incident radiation of the object to be modulated and is focused on an area equal to or smaller than the area occupied by one position index. The probe radiation transmitted or reflected from each position index is directed to a detector, which may be, for example, a photodiode. When the probe beam coincides with the first position index, a fraction of the intensity characteristic of the probe beam of the first type of position marker is incident on the detector. As the substrate is displaced relative to the first position index, the fraction of the probe beam returning to the detector falls to zero, and then as it approaches coincidence with the second position index, the fraction characteristic of the second type of position marker rises. Thus, the intensity received at the detector periodically rises in characteristic value at each position marker and falls to zero at intermediate points between the position markers. The intensity of the probe beam returning to the detector is proportional to the line frequency ν L A sampling frequency ν at least 4 times higher than s Preferably, v s / ν L>20. The intensity measured by the detector is transmitted to a digital processor, which calculates the position of the substrate relative to the center of the incident electromagnetic radiation to be modulated.

[0013] Each different type of optical element causes electromagnetic radiation incident on that element to exit that element in a different state than electromagnetic radiation incident on a different type of optical element, which may be in terms of propagation direction, phase, or polarization. At any instant in time, the aligned array is divided into active regions comprising a set of optical elements that have at least a portion of the incident electromagnetic radiation to be modulated impinging thereon, and inactive regions comprising a set of optical elements that are not impinged by any of the electromagnetic radiation to be measured.

[0014] The first type of optical element is the aperture type, where the incident electromagnetic radiation leaves this type of optical element unchanged, except for the diffractive effects at the aperture ends.

[0015] The second type of optical element is transmissive, where incident electromagnetic radiation passes through a transmissive medium with a phase change proportional to the optical thickness of the transmissive medium. Different optical thicknesses produce different phase changes and therefore represent different types of optical elements.

[0016] A third type of optical element is reflective. In this case, incident electromagnetic radiation leaves the optical element with an angle of reflection equal to the angle of incidence. To provide different angles of incidence, the orientation of the reflective element can be rotated relative to the direction of the incident electromagnetic radiation. Different angles of incidence cause the incident radiation to be reflected in different directions and therefore represent different types of optical elements. Furthermore, the reflective optical elements may be in a plane perpendicular to the direction of the incident electromagnetic radiation and may differ only in their distance from the average substrate surface. In this case, each distance from the average substrate surface produces a different phase change and therefore constitutes a different type of optical element.

[0017] A fourth type of optical element is refractive, where incident electromagnetic radiation strikes a member with a different refractive index than the first and exits the optical element at an angle that depends on the angle of incidence and the refractive index. Both the angle of incidence and the refractive index can be changed to change the angle at which the electromagnetic radiation exits, with each combination of refractive index and angle of incidence constituting a different type of optical element.

[0018] A fifth type of optical element is diffractive: in this case, incident electromagnetic radiation impinges on a set of diffraction grating lines that can have different pitches and orientations. Each difference in pitch and orientation causes the incident electromagnetic radiation to diffract and constructively interfere in a different direction, and therefore each combination constitutes a different type of optical element.

[0019] The sixth type of optical element is polarizing. In this case, incoming electromagnetic radiation impinges on polarizing optical components that can have different orientations, and with each orientation the incoming electromagnetic radiation exits with a different polarization state. Each polarizer orientation therefore constitutes a different type of optical element.

[0020] The different types of optical elements listed above may be combined to produce further types of optical elements that modify at least one property of the incident radiation.

[0021] In some embodiments the optical element is planar, while in other embodiments the optical element has a curved surface. In particular, an optical element with a curved surface may be used to focus radiation incident on said surface onto the detector location.

[0022] In the most preferred embodiment, the movable substrate is a flexible tape that translates the array of optical elements in a closed loop, where the tape is substantially flat in at least one region along the closed loop. Preferably, the tape loop is rigidly held in shape by two or more sprockets that engage the tape through a drive aperture to translate the tape at a controlled speed. The term substantially flat means that, within a tolerance of 2 degrees, the surface of the tape is parallel to a line between two of the sprockets. The surface of the flat substrate thus defined may correspond to an active area where incident electromagnetic radiation interacts with the array of optical elements. Each type of optical element functions to direct electromagnetic radiation in a common direction. In HEMS applications, each type of optical element directs electromagnetic radiation to a detector dedicated to that type. The optical elements typically have a function normal to the flat substrate that is greater than the standard deviation of the substrate surface.

[0023] In some embodiments, the tape contains regions of different optical thickness that are positioned close to each other to create an interference pattern and effect a phase shift in the incident radiation flux.

[0024] In some embodiments, the pitch of the diffractive features varies along the length of the tape. This feature can be used, for example, to vary the free spectral range of a diffractive system that alternates between exploring a broad spectrum with low spectral resolution and scanning a spectral region of interest with high spectral resolution.

[0025] In a preferred embodiment, the movable substrate is a disk, the array of optical elements is arranged in a track adjacent to the periphery of the disk around the center of rotation, and a second concentric track closer to the array of optical elements contains an array of position markers with the same angular spacing as the optical elements.

[0026] In some embodiments, the movable substrate is an arc that oscillates harmonically relative to the incident radiation, and the array of optical elements is disposed along an outer edge of the arc.

[0027] In some embodiments, the optical element transitions between at least two different types, and the transition occurs during the period when the optical element is in the inactive region. This feature allows the spatial modulator of the present invention to dynamically change the modulation scheme without loss of duty ratio due to transition time. For example, the micromirror changes from a first fixed angle to a second fixed angle during the inactive section.

[0028] In some embodiments, optical elements such as micromirrors on a spatial modulator can change orientation. The change in orientation occurs when the element is in an inactive region. For example, in a rotating disk spatial modulator with an active region of 0-10 degrees, the orientation of the optical element is fixed while in the range of 0-10 degrees. The transition occurs in the range of 10-360 degrees. In this example, the required modulation speed is reduced by a factor of 36. This configuration combines the high line frequency of a translating modulator with the flexibility of an array of dynamically adjustable micromirrors.

[0029] In some embodiments, at least some of the optical elements are comprised of materials that respond to the electro-optic effect, and a change of type is brought about by applying a voltage across the optical element. [Brief description of the drawings]

[0030] [Figure 1] FIG. 2 is a perspective view of an enlarged portion of a preferred embodiment of the present invention. [Diagram 2] FIG. 2 is a schematic diagram of the embodiment of FIG. 1 showing a closed loop. [Diagram 3] FIG. 13 is another schematic diagram of a preferred embodiment showing dynamically altered optical elements. [Figure 4a] FIG. 1 is a schematic diagram of an embodiment of a pendulum of the present invention. [Figure 4b]FIG. 1 is a perspective view of an embodiment of a disk of the present invention. [Diagram 5] 1A-1D are schematic diagrams of embodiments of a disk of the present invention showing different types of position markers. [Figure 6] The theoretical waveform and the noise waveform are plotted from the order of the position markers. [Figure 7] 1 is a flowchart illustrating a method for measuring a position. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0031] Figure 1 is a perspective view of a preferred embodiment of the present invention. A movable substrate in the form of a tape (10) translates from left to right with a velocity v in a direction represented by (30) while carrying an array (40) of optical elements (111) including components (11), (12), (13), (14), (15), (16), (17), (19) through a region (200) where incident electromagnetic radiation is incident on the substrate (10). Region (200) is designated the active region and adjacent region (201) is designated the inactive region. Optical elements in the active region (200) modulate incident electromagnetic radiation to an "on" state. Optical elements in the inactive region (201) modulate incident electromagnetic radiation to an "off" state. The portion shown is preferably part of a closed loop of total length L. The active region (200) is of length A. The optical elements of the active region direct incident EM radiation in a direction specified by the type of optical element for a time A / v with a repeat period L / v.

[0032] The optical element (11) is an aperture through which the incident EM radiation can pass substantially unchanged, except for diffraction effects at the aperture edges. Diffraction effects are minimal if the sides of the aperture are much larger than the wavelength of the incident EM radiation. The aperture (11) is in a non-active region (201) and therefore at the instant shown no EM radiation passes through it. However, when the substrate (10) is subsequently translated in the direction (30), the aperture (11) enters the active region (200). Only when the aperture (11) is in the active region (200) does transmission occur through the aperture (11) and therefore modulation is achieved.

[0033] The optical elements (12), (13) are diffraction gratings of different pitches. For each wavelength, the incident EM radiation is diffracted into multiple orders. For order 0, the EM radiation is reflected by the diffraction gratings (12), (13) in the same direction. For orders other than 0 (i.e., + / -1), the diffraction gratings (12), (13) diffract the incident EM radiation into different angles. All of the diffraction grating (12) is in the non-active area (201), so no EM radiation is observed at the angle determined by the pitch of the diffraction grating (12). The diffraction grating (13) is partially in the active area (200), so as long as the diffraction grating (13) remains within the active area (200), it directs the incident EM into an angle determined by the pitch of the grating. The optical elements (12), (13) may be diffraction gratings made up of an array of dynamically adjustable micromirrors whose pitch can be changed by changing the orientation of the rows of micromirrors while in the inactive region (201).

[0034] The optical elements (14), (15) are mirrors tilted at different angles with respect to the incident EM radiation (100), so that while the mirrors (14), (15) are in the active area (200), the EM radiation is reflected at different angles. Detectors, each positioned at the appropriate reflection angle, observe the reflected EM radiation, whose mere presence represents, for example, a binary "1". As the substrate tape (10) translates in the direction (30), the optical element (15) enters the inactive area (201), and after a while the optical element (15) retracts from the inactive area (201). The absence of reflected EM radiation represents, for example, a binary "0". In some embodiments, the tilt angle of the mirror elements (14), (15) can be changed while the elements are in the inactive area (201).

[0035] The optical elements (16), (17) are reflective mirrors parallel to the surface of the substrate. Incident EM radiation is reflected by each at the same angle, but with different phases due to the difference in elevation above the average substrate plane. The optical elements (16), (17) may be, for example, part of a Fabry-Perot filter or a Fabry-Perot interferometer. The optical elements (16), (17) may be, for example, part of a step-scan Michelson interferometer. As shown, the optical elements (16), (17) are in an active region (200). As the optical elements (16), (17) translate in the direction (30), they enter a non-active region (201), but in some embodiments the elevation of the mirror surface can be changed to provide a different phase shift in the next repeat period of the element L / v.

[0036] The optical element (19) is a dispersive prism with an adjacent buffer region (18), both of which are located in the non-active region (201). When the prism is in the active region (200), incident EM radiation is refracted at an angle determined by the prism geometry and the refractive index of the prism. In some embodiments, the buffer region (18) is used to provide an unobstructed optical path to adjacent optical elements. In some embodiments, the optical elements do not abut the buffer region at all.

[0037] An array of positional indicia is shown at (20) adjacent and parallel to the array of optical elements (40). As shown, the positional indicia is an aperture that transmits a probe beam (not shown) when a portion of the aperture intersects the probe beam. A detector (not shown) measures the intensity of the transmitted probe beam and a computing device calculates the position of the substrate relative to the probe beam.

[0038] The example shown in FIG. 1 can be used in a multi-spectrometer, for example as described in the HEMS application cited above.

[0039] FIG. 2 is a schematic top view of the configuration shown in FIG. 1. The tape substrate (10) forms a closed loop around sprockets (51), (52), (53). The tape carries optical elements including mirrors, indicated at (14), (15), with different tilt angles, and an aperture (11). The incident EM radiation (100) to be modulated is incident on a substantially flat active area (200) between the sprockets (51), (53). The incident EM radiation may be dispersed across the active area (200) by wavelength, for example in HEMS applications. The modulated EM radiation from the aperture element (11) travels in a direction (31) and is observed at a detector (41). The modulated EM radiation from the mirror element (14) travels in a direction (34) and is observed at a detector (44). The modulated EM radiation from the mirror element (15) travels in a direction (35) and is observed at a detector (45). For illustrative purposes, the detectors (44), (45) are depicted in the plane of the tape substrate (10). In a preferred embodiment, the mirrors (14), (15) are tilted in a direction perpendicular to the direction of belt motion, and the detectors (44), (45) are above and below the plane of the drawing. A probe beam (101) is generated by a light source (80), the portion of which transmitted through an aperture (not shown) in the position index produces a beam (102), which is received by a photodiode (81) and converted to a digital amplitude by an analog-to-digital converter (82). The sequence of the digital amplitude is analyzed by a computing device (83), which outputs a digital representation of the substrate tape position (84) for transmission to a user. The position information is important for operating an optical device based on the spatial modulator of the configuration herein, because the exact spatial modulator configuration that can be operated can be calculated from the position information and knowledge of the spatial modulator geometry. For HEMS applications, for example, the width of the aperture (11) and mirrors (14), (15) is 50 microns along the tape advance direction, and the tape substrate speed is 50 m / s to achieve a modulation rate of 1 MHz. Using this example configuration, a spectrum with 1000 wavelength channels can be measured in 1 ms. Higher and lower modulation rates can be produced by the configuration of Figure 2.

[0040] Figure 3 is a schematic diagram of the tape substrate shown in Figure 1. Three types of optical elements (13), (14), (15) (with different shading) are aligned along the tape axis moving in the direction (30). The active area is represented by (200). The optical element (14) is a movable mirror in the non-active area (201), shown enlarged in (24), which rotates to a new position about a pivot (25). The position indicator (20) is located in a line parallel to the array of optical elements (40). To translate the tape substrate (10), the two rows of apertures (21) shown in Figure 3 engage with sprockets (51), (52), (53) shown in Figure 2.

[0041] Figure 4a shows an alternative configuration in which an array of optical elements (111) as best shown in Figure 1 is mounted on a substrate (301) carried by a harmonically oscillating pendulum or rod (300). The rod may, for example, be excited and vibrated at the resonant frequency of the MEMS device. For sub-millimeter scale MEMS devices, vibration is technically easier to achieve than linear translation. The optical elements may be mounted along an arc in a plane swung by the arm of the pendulum, or in an arc in a plane perpendicular to the axis of the pendulum. The example shown in Figure 4a can be used in a multispectrometer, for example as described in HEMS applications.

[0042] Figure 4b shows a perspective view of an embodiment in which an array of optical elements (111) is mounted around the circumference of the disk (112) perpendicular to the plane of the disk. In this configuration, the optical elements are at a constant radius with respect to the incident radiation and of a constant preset width. Optical elements arranged to fill the space in the plane of the disk are generally wedge-shaped and distort the resolution of the HEMS spectrometer. The distortion can be reduced below a threshold by increasing the radius at which the optical elements are located.

[0043] Figure 5 shows a top view of a substrate (10) in the shape of a disk (28) with an axis of rotation (27) in the direction of rotation (31). The active area is designated (200). The disk substrate (10) carries three differently shaded types of optical elements (13), (14), (15) arranged to form a code sequence of length 10 in the active area (200). The three different types of position indicators have different radial dimensions and are designated (74), (75), (76). The position markers (74), (75), (76) transmit different amplitudes of the probe beam, best shown in Figure 2. In the illustrated example, the position marker (75) with the largest radial dimension represents the beginning of the code sequence, and the position markers (74), (76) represent the binary values ​​"0" and "1", respectively, used to label each sector of the code sequence. The position marker (76) is distinguished from the position marker (74) by its larger radial length. The values ​​assigned to the position markers of different lengths are interchangeable and there may be multiple lengths representing multiple values. In noisy environments, the binary level as shown is the most robust. In the illustrated example, the sector labels of the active area are represented by the position indices (76), (77) as a binary "11". In the illustrated example, a two-digit binary number is sufficient to uniquely label all sectors. More binary numbers may be used. The beginning and end of the sector labels are referenced by their displacement relative to the index peak (75). The sector labels as illustrated are adjacent to the index peak (75), but may occur anywhere between the index peaks. The area of ​​the sector label between the first and second index peaks is preferably closer to the first index peak, in which case a translational or rotational direction can be determined. The example shown in FIG. 5 can be used in a multi-spectrometer, for example as described in a HEMS application.

[0044] FIG. 6 shows the theoretical waveform received by detector (81) of FIG. 2 (lower curve) and the corresponding waveform with noise added (upper curve). The main peak corresponds to the position marker marking the beginning of the code string, best shown in FIG. 5 as (75), and the main peak is designated as the index peak. The remaining peaks correspond to the position markers (74) of FIG. 5. Some of the position markers (74) may be used as sector identifiers, in which case they are all of the same value. When analyzed with a prior art comparator, noise causes the periodicity of the peak positions to vary. When a threshold is reached, the comparator is triggered. Noise in the signal shifts the position of the threshold, and noise in the comparator may shift the threshold itself. In the present invention, by sampling the position marker waveform at a frequency much higher than the frequency of the waveform to obtain at least four points per peak, and preferably more than twenty. In the simulation, a higher sampling rate reduces the difference between the measured position and the actual position and can improve the resistance to noise effects. The peaks are numbered consecutively, starting from the index peak.

[0045] As shown in Figure 7, once the approximate frequency and phase of the waveform are known, the location of the approximate minimum of the waveform relative to the index peak can be calculated and used as an upper integration limit to calculate the area and moment of the peak. The peak moment is calculated as the sum of the displacement (in fractional units of the peak width) from the index peak multiplied by the amplitude of the peak measured at each displacement during the approximate minimum displacement. The area of ​​the peak is the sum of the amplitudes of the peaks during the approximate minimum displacement. The peak center is calculated as the peak moment divided by the area. The locations of the N peak centers are obtained, and then a least squares regression is performed to correlate the number of peaks with the peak center. The slope and intercept of the regression give the frequency and phase, respectively. These improved frequency and phase approximations are used to calculate the next set of minima; i.e., for each iteration of the algorithm, from the peak position measured under noise to the actual peak position. The position of the board can be calculated from the frequency, phase, and number of clock ticks (measured by the ADC) since the most recent index peak. The accuracy achieved is approximately 20% of the translation between ADC measurements, translating to approximately 1% of the optics dimension with 20 measurements per line period.

Claims

1. 1. A method for spatially modulating electromagnetic radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation towards an ordered array of optical elements carried on a substrate; translating the substrate to associate the incident radiation with at least a portion of each of two different ones of the optical elements such that at two different times, each of the two different optical elements is associated with the incident radiation; generating position measurements of the position of the substrate at a plurality of times between the two different times; and transmitting the generated position measurements to a user; A method according to claim 1, wherein the array of optical elements comprises at least three optical elements and at least two optical elements that modulate the radiation incident thereon in different ways.

2. 10. The method of claim 1, wherein the optical elements of a spatial modulator direct electromagnetic radiation to be modulated in at least two different directions.

3. 10. The method of claim 1, wherein the optical elements of a spatial modulator direct electromagnetic radiation to be modulated in at least three different directions.

4. The method according to any one of claims 1 to 3, characterized in that the optical elements of the spatial modulator bring about at least two different phase changes in the electromagnetic radiation to be modulated.

5. The method according to any one of claims 1 to 4, characterized in that the optical elements of the spatial modulator bring about at least three different phase changes in the electromagnetic radiation to be modulated.

6. Method according to any of the claims 1 to 5, characterized in that the optical elements of the spatial modulator change the polarization of the incident radiation to be modulated in at least two different ways.

7. Method according to any of the preceding claims, characterized in that the optical elements of the spatial modulator change the polarization of the incident radiation to be modulated in at least three different ways.

8. A method according to any one of claims 1 to 7, characterized in that the optical elements of the spatial modulator are integral with the substrate material.

9. The method according to any of the preceding claims, characterized in that the optical element is selected from the set of apertures, mirrors, diffraction gratings, phase plates, refractive wedges, refractive prisms and polarizers.

10. The method according to any of the preceding claims, characterized in that the optical element comprises a mirror capable of assuming at least two different configurations.

11. 10. The method of claim 9, wherein at least one of the optical elements undergoes at least one change in configuration, the change in configuration occurring when the optical element is not exposed to the electromagnetic radiation to be modulated.

12. A method according to any of the preceding claims, characterized in that the step of measuring the position uses a component which is integral with the substrate and in the vicinity of the optical element.

13. 13. The method according to claim 1, wherein the substrate is a flexible tape forming a closed loop, the flexible tape being translated around the closed loop, and the optical element being positioned along the translation direction.

14. A method according to any of the preceding claims, characterized in that the substrate is a rotating disk and the optical elements are arranged at a common radial distance from an axis of rotation.

15. A method according to any one of claims 1 to 14, characterized in that the substrate is a circular arc which rotates periodically and / or reciprocally about an axis of the circular arc, and the optical elements are arranged along the circular arc at a common radial distance from the axis of rotation.

16. The generating of the position measurements comprises: Directing a light beam at the substrate having an array of reflective or transmissive position indicators; moving the substrate relative to the light beam so as to transmit or reflect portions of the light beam from at least two different position markers at different times; measuring the intensity of the transmitted or reflected light at a plurality of time intervals; analysing the measured light intensity multiple times to provide said position measurement.

17. 17. The method of claim 16, wherein the light beam intersects zero or one position marker at a given moment, and wherein the light beam intersects at least two different position markers at different moments.

18. the intensity of the light beam transmitted or reflected from each position marker is measured at least four times and at at least four different positions on the substrate; 18. The method of claim 17, wherein at least a portion of the light transmitted or reflected from the position marker is included in each measurement.

19. the intensity of the light beam transmitted or reflected from each position marker is measured at least 20 times and at at least 20 different positions on the substrate; 18. The method of claim 17, wherein at least a portion of the light transmitted or reflected from the position marker is included in each measurement.

20. A method according to any one of claims 16 to 19, characterized in that the position measurement of the substrate is calculated by performing a least squares fit to the locations of at least three position markers.

21. A method according to any of claims 1 to 20, characterized in that there are at least two types of position markers which transmit or reflect different parts of the probe light beam, and the difference in intensity is analysed to provide information about the position of the substrate.

22. 9. The method of claim 8, wherein the optical elements are fabricated on the substrate member by a subtractive process.

23. 9. The method of claim 8, wherein the optical element is fabricated on the substrate member by an additive process.

24. 1. A method for spatially modulating electromagnetic radiation to measure one or more dependent variables of incident radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation towards an ordered array of optical elements carried on a substrate; translating the substrate to associate the incident radiation with at least a portion of each of two different ones of the optical elements such that each of the two different optical elements is associated with the incident radiation, the optical elements being arranged to direct the incident radiation into at least two paths; generating position measurements of the position of the substrate at at least two different times; calculating a modulation configuration from said position measurements; measuring a total intensity of said radiation in each path with a detector in each modulation configuration to provide a plurality of detector outputs; analyzing the detector output in relation to a modulation configuration to obtain information regarding a dependent variable of the radiation being measured; The method, wherein the array of optical elements comprises at least three optical elements and at least two optical elements that modulate the radiation incident thereon in different ways.

25. 1. A method for spatially modulating electromagnetic radiation, the method comprising: collecting electromagnetic radiation of a spatially modulated object; directing the radiation towards an ordered array of optical elements carried on a substrate; translating the substrate to change the portion of the ordered array of optical elements exposed to the radiation such that incident radiation engages at least a portion of each of two different optical elements at two different times; generating position measurements of the position of the substrate at least at the two different times; and transmitting the generated position measurements to a user; the array of optical elements includes at least three of the optical elements, and at least two of the optical elements modulate the incident radiation in different ways; The optical element can have at least two different configurations; A method, wherein at least one of the optical elements changes configuration at least once, the change in configuration occurring when the optical element is not exposed to modulated electromagnetic radiation.

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