CN101799590A - Digital Fresnel method and device for eliminating black-matrix effect of phase spatial light modulator (PSLM) - Google Patents
Digital Fresnel method and device for eliminating black-matrix effect of phase spatial light modulator (PSLM) Download PDFInfo
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Abstract
The invention discloses a method for eliminating the black-matrix effect of a phase spatial light modulator (PSLM) by using a digital Fresnel lens. In the method, by superposing the digital Fresnel lens on a phase modulation graph, the light gathering action of the Fresnel lens is used for separating the position of the diffraction image of the phase modulation graph from the position of the diffraction image of a black matrix, thereby overcoming the black-matrix effect of the spatial light modulator. Firstly, the digital Fresnel lens is superposed on the phase modulation graph to enable the effective optical information corresponding to the phase modulation graph to be imaged on the focal plane of the Fresnel lens, and meanwhile, the phenomena of central strong bright spots and advanced diffraction bright spots caused by the black-matrix effect are not formed, thereby realizing the purpose of inhibiting the black-matrix effect of the PSLM only by digital compensation, and improving the practical application value in optical information processing.
Description
Technical Field
The invention relates to a method for eliminating the black grid effect of a phase type spatial light modulator, belonging to the optical information processing technology.
Background
A Spatial Light Modulator (SLM) is a device that can modulate a certain parameter of an optical wave under the control of a signal source, and for example, modulates an amplitude by absorption, modulates a phase by a refractive index, and modulates a polarization state by rotation of a polarization plane. The optical parallel, interconnection and high-speed processing capability is effectively utilized, so that the optical parallel, interconnection and high-speed processing capability can be used for modulating light beams in real time on space, the optical parallel, interconnection and high-speed processing capability becomes a core component of a system for real-time optical information processing and the like, has more and more important position and value in the modern optical field, and is a basic component and a key device in researches on optical interconnection, optical correlation, optical calculation, mode recognition, optical control, optical detection, image processing, display technology and the like of an optical and photoelectric hybrid system.
The modulation method by the SLM is mainly classified into two types, one is an amplitude modulation type and the other is a phase modulation type. The amplitude modulation SLM modulates the amplitude of an incident light wave by conversion of its transmittance or reflectance, and is mainly used for applications such as optical switching, filtering, and optical correlation. The SLM is increasingly gaining importance in optical information processing, and is widely used mainly because it can implement phase modulation, which can change the intensity change of an image into the refractive index change of the SLM, thereby modulating the phase. The phase, which cannot be directly characterized by the intensity, can thus be implemented by means of an intensity image by means of an SLM to achieve the phase modulation effect. Thus, a wide range of optical information processing systems, especially some of the latest technologies such as computer holography, diffractive optics, beam shaping, optical tweezers, etc., use phase-type spatial light modulation.
Spatial light modulators are typically composed of individual discrete pixels, and the variation of each pixel can be independently controlled to achieve pixel-by-pixel modulation of the light wave front. A digital image for modulating the light wave is written to the SLM, which displays the image, and the incident light wave is spatially modulated as it passes through the SLM. However, since each pixel is surrounded by an electrode, the non-light-transmitting regions are formed on the SLM in a criss-cross manner, so that the device is arranged in a two-dimensional periodic grid structure. The light waves are diffracted by the two-dimensional grating structure, which brings about two problems: the central bright spot and the multi-order diffraction image, especially the central bright spot, have much higher intensity than the other diffraction orders due to the high concentration of energy. This phenomenon is referred to as the "black grid effect" of the spatial light modulator.
The "black grid effect" is a phenomenon inherent to the SLM, and exists even when no image is written into the SLM, and when a modulation image is written, the center of the diffraction image of the written image coincides with the central bright spot, and the center of the higher-order diffraction image also coincides with the higher-order diffraction bright spot of the spatial light modulator, so that the center of the image on the receiving surface is always coupled with the inherent multi-order diffraction bright spot of the spatial light modulator and cannot be separated, and the quality of the diffraction image is seriously reduced, or even cannot be used. This effect affects the application of the spatial light modulator, and brings about an extremely adverse effect on the application of the spatial light modulator, so that the application of the spatial light modulator in optical information processing is greatly limited.
Therefore, a method capable of suppressing the black grid effect is sought, which is of great value for the application of the spatial light modulator in optical information processing.
Disclosure of Invention
The invention aims to provide a method capable of eliminating the black grid effect of a phase type spatial light modulator, which improves the phase modulation performance of the spatial light modulator.
The invention is realized by the following technical scheme: the digital Fresnel lens is superposed on the phase modulation graph, and the focusing effect of the Fresnel lens is utilized to separate the diffraction image of the phase modulation graph from the imaging position of the diffraction image of the black grating so as to overcome the black grating effect of the spatial light modulator, and the method is characterized by comprising the following steps of: the incident light wave is converted into linearly polarized light by the polarizer, the linearly polarized light is incident to the light receiving surface of the spatial light modulator, the spatial light modulator works in a phase modulation state, an analyzer is arranged behind the spatial light modulator, the included angle between the polarizer and the polarization axis of the analyzer is adjusted, the spatial light modulator works in the phase modulation state, and the light intensity transmitted by the analyzer does not change along with the phase modulation degree; superposing a digital Fresnel lens on a phase modulation diagram for modulating incident light waves, writing the superposed phase modulation diagram into a spatial light modulator, wherein the light waves are refracted by the Fresnel lens, a diffraction image corresponding to the phase modulation diagram can be received on a Fresnel lens focal plane, and the focal length of the digital Fresnel lens is adjusted to receive and observe diffraction imaging results of the phase modulation diagram at different positions; the two-dimensional periodic grating structure of the spatial light modulator is not affected by digital operation, a 'black grating effect' is not formed at the position of a focal plane of an added digital Fresnel lens, light waves diffracted by the black grating are transmitted to the digital Fresnel lens, and only one uniform background light is formed according to the Fresnel diffraction effect, so that the background of a received diffraction image is brighter, and the diffraction image of a phase modulation graph and the diffraction image of the black grating are completely separated along the direction of an optical axis, so that the influence of the 'black grating effect' is eliminated, and the modulation performance of the spatial light modulator is improved.
Before writing the phase modulation pattern into the SLM, a computer-generated digital fresnel lens is superimposed on it, and the result of the diffraction imaging is observed in the focal plane of the added fresnel lens. Because of the convergence effect of the Fresnel lens, the diffraction image corresponding to the phase modulation image is imaged on the focal plane of the Fresnel lens, and the Fresnel lens has no influence on the black grating effect of the spatial light modulator, so that the black grating effect, namely the central bright spot and the high-grade diffraction image, on the focal plane of the Fresnel lens is not formed, the influence brought by the black grating is only to form uniform background light, the background light only can influence the contrast of the diffraction image of the phase modulation image, and the adverse effect brought by the black grating is far smaller than that of the central bright spot.
A device for eliminating black grid effect of a phase type spatial light modulator by using a digital Fresnel lens is characterized in that: the device is composed of the following structures: the light source (201) generates incident light waves, and the incident light waves are expanded into parallel light beams after passing through the first lens (202) and the second lens (203); the parallel light beams are converted into linearly polarized light through a polarizer (204), the linearly polarized light passes through a transmission type spatial light modulator (205), the spatial light modulator carries out phase modulation on the linearly polarized light, the modulated light beams pass through an analyzer (206) and enter an image detector (207), and imaging of the modulated light beams is detected by the image detector (207); the central processing unit (208) receives the input phase modulation graph and superposes a digital Fresnel lens on the phase modulation graph, the diffraction image of the phase modulation graph is separated from the imaging position of the diffraction image of the black grating by utilizing the convergence effect of the Fresnel lens, the imaging is received at the position of the diffraction image of the phase modulation graph superposed with the digital Fresnel lens, the light wave diffracted by the black grating is spread at the position, only uniform background light is formed, the background of the received diffraction image is brighter, and the influence of the black grating effect is eliminated.
The digital Fresnel lens does not have any influence on the two-dimensional periodic structure of the SLM, the black grid effect still exists, but the black grid effect is the result of Fraunhofer diffraction of the inherent two-dimensional periodic structure of the SLM, so that the black grid effect is not formed on the focal plane of the Fresnel lens, and the light waves diffracted by the black grid are spread to the position to form only one uniform background light, so that the background of the received diffraction image is brighter, the image contrast is reduced, but the adverse influence brought by the black grid effect is far smaller than the central bright spot brought by the black grid effect, and the black grid effect of the spatial light modulator is well overcome by the method.
The spatial light modulator may be a transmissive type or a reflective type, and in the case of a reflective type SLM, the SLM may be operated in a normal incidence state by a single beam splitter prism. The operating state at normal incidence is not a necessary condition, but is intended to constitute a coaxial optical system for ease of adjustment.
The digital Fresnel lens is produced by a computer, optical parameters such as focal length and the like can be conveniently changed according to the design requirements of an actual optical system, and the digital Fresnel lens is directly superposed on a phase modulation diagram after being generated by the computer.
Compared with the prior invention and technology, the invention has the following advantages:
the digital Fresnel lens is superposed on the phase modulation graph, and the diffraction image corresponding to the phase modulation graph and the diffraction image corresponding to the spatial light modulator black grid are separated in the optical axis direction by utilizing the gathering effect of the Fresnel lens, so that the black grid effect of the phase type spatial light modulator is eliminated. The digital Fresnel lens used by the technology is generated by computer calculation and is superposed on a phase modulation graph, the process is completely automatically completed by a computer, optical parameters such as the size, the focal length and the like of the lens are changed in a digital domain, the digital Fresnel lens is completed by the computer through setting, the black grid effect of the phase type spatial light modulator is eliminated, meanwhile, devices such as additional Fourier lenses or filters and the like are not needed, and the structure is simple.
Drawings
Fig. 1 is a schematic diagram of a physical structure of a spatial light modulator. Wherein the white areas represent light-transmitting portions and the black areas represent light-non-transmitting portions.
FIG. 2 is a schematic diagram of the principle of eliminating the black grid effect by digital Fresnel.
FIG. 3 is a graph of intensity contrast between Fresnel diffraction and Fraunhofer diffraction for a spatial light modulator. Wherein the dotted line is the Fresnel diffraction intensity curve and the solid line is the Fraunhofer diffraction intensity curve.
Fig. 4 is a schematic diagram of the principle of operation of a transmissive spatial light modulator.
Fig. 5 is a schematic diagram of the operation of a reflective spatial light modulator.
FIG. 6 shows the result of diffraction imaging before the spatial light modulator is added to the digital Fresnel lens.
FIG. 7 shows the result of diffraction imaging of a spatial light modulator with the addition of a digital Fresnel lens.
FIG. 8 is an embodiment of a spatial light modulator after the addition of digital Fresnel lenses of different focal lengths.
In the figure, 101 is an initial phase modulation diagram, 102 is a diffraction image corresponding to an ideal case, 103 is a diffraction image under the influence of the black grid effect of the spatial light modulator, 104 is a digital fresnel lens, and 105 is a diffraction image added with the digital fresnel lens.
In the figure, 201 is a light source, 202 is a first lens, 203 is a second lens, 204 is a polarizer, 205 is a transmissive spatial light modulator, 206 is an analyzer, 207 is an image detector, 208 is a central processing unit, 209 is a beam splitter prism, and 210 is a reflective spatial light modulator.
Detailed Description
The following describes the embodiments in further detail with reference to the accompanying drawings.
FIG. 1 is a schematic diagram of the physical structure of a spatial light modulator with white areas representing light-transmissive portions, also representing each pixel; the dark areas represent opaque parts and the inherent physical structure causes the SLM to assume a two-dimensional grid structure. The influence of the black grid effect of the SLM is mainly in the fraunhofer diffraction area, so the black grid effect can be seen as fraunhofer diffraction of a two-dimensional grid, and its fraunhofer diffraction field on the fourier spectral plane of the lens focal length can be seen as the fourier transform of an array of rectangular holes.
Defining a line-direction coordinate f on the SLMxThe column direction coordinate is fyW is the spacing between pixel centers of the SLM, w0For the width of the pixel opening of the SLM, the transmittance function of each pixel is
The transmission function of the SLM over M rows and N columns is
Transmittance function T (f) of black gridx，fy)：
In plane wave U0(fx，fy) Under illumination, the complex amplitude distribution of the multiplication of the plane wave and the black grid transmittance function is:
the fraunhofer diffraction pattern on the fourier spectral plane is:
wherein,
by theoretical derivation of equations (1) - (4), the two-dimensional grid on the SLM has a convolution modulation of the fraunhofer diffraction pattern of the incident plane wave on the fourier spectral plane. This is determined by the physical structure of the SLM, and this effect exists regardless of any information input. However, since the black grid effect is the result of fraunhofer diffraction, if observed or received in the near field, the phase modulation pattern and the diffraction image of the black grid propagate a certain distance in the form of fresnel diffraction, at this time, if a digital fresnel lens is superimposed on the initial phase modulation pattern, the diffraction image corresponding to the phase modulation pattern is observed on the focal plane, and at this time, the black grid effect is not formed yet. Therefore, a schematic diagram of a method for eliminating the SLM black grid effect by using a digital fresnel lens is shown in fig. 2.
Fig. 2 is a schematic diagram of the principle of eliminating the black grid effect by phase compensation. The diffraction imaging result of the phase modulation diagram 101 in the ideal case is shown as 102, and after the phase modulation diagram 101 is written into the spatial light modulators 205 and 210, the diffraction imaging result is shown as 103 due to the black grid effect of the spatial light modulators 205 and 210, and as shown in the figure, the black grid effect causes the central bright spot and the high-level diffraction image to be coupled with the effective light information and cannot be separated. In the present invention, a digital Fresnel lens 104 is superimposed before writing a phase modulation pattern 101 into spatial light modulators 205, 210, and when the diffracted image is distributed in U 'on the back focal plane of the lens'f(x, y) is:
wherein U (x)1，y1) For the phase modulation chart of the input, (x)1，y1) Is the input surface coordinate, (x, y) is the output surface coordinate, λ is the wavelength, and f is the focal length. Then, as can be seen from equation (5), the field distribution at the focal plane is the fraunhofer diffraction pattern of the field incident on the fresnel lens. At the moment, the field distribution of the black grid on the rear focal plane of the Fresnel lens is Uf″(x，y)：
Wherein U' (x)1，y1) As a function of the spatial light modulator, the field distribution of the black grid in the focal plane of the fresnel lens is known from equation (6) as its fresnel diffraction pattern. As shown in fig. 3, the fresnel diffraction intensity and fraunhofer diffraction intensity of the simulated spatial light modulator in the focal plane of the fresnel lens are represented as a dotted line and a solid line, respectively, and are shown in the same coordinate system. From fig. 3, it can be seen that the diffraction field at the focal plane position of the fresnel lens has an intensity much less than that of fraunhofer diffraction, and the intensity distribution can be considered approximately as uniform, which is a background intensity on the observation or receiving surface, and the effect is shown as 105 in fig. 2, and the received image has a brighter background but does not have a serious central bright spot problem.
The phase factor of the digital Fresnel lens added is exp [ j π/λ f (x)1 2+y1 2)]This is used as a phase compensation template 104, multiplied by a phase factor corresponding to the original phase modulation pattern 101, and the superimposed result 105 is written into the SLM. The value range of the focal length of the lens depends on two factors: first, the focus size is such that diffraction of the two-dimensional grid of the spatial light modulator is ensuredThe approximate condition of Fresnel diffraction is met, namely the distance which can not be close to the far field diffraction distance of Fraunhofer because the focal distance is too large; the second is the limitation of sampling on the minimum focal length of the fresnel lens, because the maximum spatial frequency of the phase factor increases with decreasing focal length, which is too small, resulting in the sampling theorem not being satisfied.
First considered in terms of propagation distance. When fresnel diffraction is established, f is satisfied:
the fraunhofer diffraction approximation condition is:
the focus value range is fnAnd fhIn the meantime. From the viewpoint of satisfying the sampling theorem, assuming that the sampling interval (or pixel size) of the spatial light modulator is d and the number of pixels is N × N, the maximum spatial frequency of the fresnel lens function on the spatial light modulator is:
according to the sampling theorem, the sampling interval is less than the reciprocal of the maximum spatial frequency of the sampling function, i.e. d is less than or equal to 1/epsilonmaxFrom this, it follows that the constraints on the focal length of the lens are:
therefore, the maximum value of the focal length of the digital Fresnel lens is less than fhThe minimum value is fnAnd fcThe larger of them.
According to the method, the system for realizing the black grid effect suppression of the phase type spatial light modulator mainly comprises a light source, the spatial light modulator, a polarizer, an analyzer, a spatial filter, an image detector and a central processing unit. The light source may be a coherent light source or a partially coherent light source; the spatial light modulator can be a reflection type or a transmission type; the polarizer and the analyzer are a pair of polarizing devices and are mainly used for ensuring the phase modulation state of the spatial light modulator; the image detector can be a CCD device or a CMOS device; the central processing unit is the combination of a digital signal processor and a programmable special integrated circuit, and can be a computer or an embedded system. The method is characterized in that a phase modulation image generated by calculation of a central processing unit is written into a spatial light modulator after being superposed with a digital Fresnel lens, is diffracted under the irradiation of incident light waves, is received by an image detector on a focal plane corresponding to the digital Fresnel lens, and then is stored and displayed by the central processing unit.
The embodiments are further described below with reference to the accompanying drawings.
Fig. 4 is a schematic diagram of the operating principle of the transmissive spatial light modulator. As shown in the figure, a light wave output by the light source 201 is expanded and collimated by an expanded beam collimating system composed of a first lens 202 and a second lens 203, the light wave is made to enter the transmissive spatial light modulator 205 in a linearly polarized light mode through the polarizer 204, the light wave passes through the transmissive spatial light modulator 205 and then passes through an analyzer 206, the polarizer 204 and the analyzer 206 are used for ensuring that the incident light wave is linearly polarized light, and the transmissive spatial light modulator 205 works in a phase modulation state under the condition of the linearly polarized light entering. The central processor 208 generates or writes the stored phase modulation pattern to the transmissive spatial light modulator 205 after superimposing the digital fresnel lens thereon, and receives and displays the diffraction imaging result transmitted from the image detector 207.
Fig. 5 is a schematic diagram of the operation principle of the reflective spatial light modulator. As shown in the figure, a light wave output by the light source 201 is expanded and collimated by an expanded beam collimating system composed of a first lens 202 and a second lens 203, the light wave is made to enter a beam splitter prism 209 in a linearly polarized manner by a polarizer 204 and then is split into two beams, wherein a transmitted beam is modulated and reflected by a reflective spatial light modulator 210, then reflected by the beam splitter prism 209 and then enters an analyzer 206. The central processor 208 generates or writes the stored phase modulation pattern into the reflective spatial light modulator 210 after superimposing the digital fresnel lens thereon, and receives and displays the diffraction imaging result transmitted from the image detector 207.
Figure 6 is the result of diffractive imaging of a spatial light modulator before the addition of a digital fresnel lens. Wherein (a) is the original image, (b) is the calculated phase diagram of the diffractive optical element corresponding to the diagram (a), and (c) is the result of diffraction imaging after the diagram (b) is directly written into the SLM, and the central bright spot is obviously visible due to the existence of the black grid effect.
FIG. 7 shows the diffraction imaging of a spatial light modulator with the addition of a digital Fresnel lens. Wherein (a) is the image after superimposing the digital fresnel lens to fig. 6(b), and (b) is the result of diffraction imaging after the image is written into the SLM, it is clear that the central bright spot has been eliminated, the influence of the black grid is only to make the background of the image brighter, and the modulation performance of the spatial light modulator is significantly improved compared to fig. 6 (c).
FIG. 8 is the result of a spatial light modulator incorporating digital Fresnel lenses of different focal lengths. The size of the added digital Fresnel lens is 512 multiplied by 512 pixels, the pixel interval d is 19 microns, the light wavelength of the laser is 532nm, the focal length f is calculated to be in the range of 0.2-45 m according to formulas (7) - (10), the focal length f is an application range of theoretical calculation, and in combination with practical use conditions, typical values are only required to be larger than a minimum value and convenient to observe or image, the focal length is too large, and the black grid effect is gradually enhanced along with the increase of the diffraction distance, so that the imaging quality is affected. In the embodiment, the focal lengths f are 300mm, 350mm, 400mm, 450mm and 500mm, respectively, which correspond to the graphs (a), (b), (c), (d) and (e). The reproduced image is observed on the focal plane, and as shown in the figure, because a Fourier lens is not used in the invention, the black grid phenomenon can be only formed in Fraunhofer far-field diffraction, and the imaging results corresponding to the phase modulation graphs are clear for digital Fresnel lenses with different focal lengths.
Claims (10)
1. A method for eliminating the black grid effect of a phase type spatial light modulator is characterized in that: the method is characterized in that a digital Fresnel lens is superposed on a phase modulation pattern, and a diffraction image of the phase modulation pattern is separated from an imaging position of a diffraction image of a black grating by utilizing the concentration effect of the Fresnel lens so as to overcome the black grating effect of a spatial light modulator, and the method comprises the following steps: the incident light wave is converted into linearly polarized light by the polarizer, the linearly polarized light is incident to the light receiving surface of the spatial light modulator, the spatial light modulator works in a phase modulation state, an analyzer is arranged behind the spatial light modulator, the included angle between the polarizer and the polarization axis of the analyzer is adjusted, the spatial light modulator works in the phase modulation state, and the light intensity transmitted by the analyzer does not change along with the phase modulation degree; superposing a digital Fresnel lens on a phase modulation diagram for modulating incident light waves, writing the superposed phase modulation diagram into a spatial light modulator, collecting the light waves through the digital Fresnel lens, receiving a diffraction image corresponding to the phase modulation diagram on a Fresnel lens focal plane, and adjusting the focal length of the digital Fresnel lens to receive and observe diffraction imaging results of the phase modulation diagram at different positions; the two-dimensional periodic grating structure of the spatial light modulator is not influenced by digital operation, a black grating effect is not formed at the position of a focal plane of an added digital Fresnel lens, light waves diffracted by the two-position grating are transmitted to the position, and because the Fresnel diffraction effect only forms uniform background light, the background of a received diffraction image is brighter, so that the diffraction image of a phase modulation graph and the diffraction image of the black grating are completely separated along the direction of an optical axis, the influence of the black grating effect is eliminated, and the modulation performance of the spatial light modulator is improved.
2. The method of eliminating the black-grid effect of a phase type spatial light modulator according to claim 1, wherein: the diffraction imaging of the phase modulation pattern on the focal plane is completed by the action of the digital Fresnel lens, without using an additional Fourier lens.
3. The method of eliminating the black-grid effect of a phase type spatial light modulator according to claim 1, wherein: the spatial light modulator described above is a transmissive spatial light modulator.
4. The method of eliminating the black-grid effect of a phase type spatial light modulator according to claim 1, wherein: the spatial light modulator described above is a reflective spatial light modulator.
5. The method of eliminating the black-grid effect of a phase type spatial light modulator according to claim 1, wherein: the digital fresnel lens described above is produced by a computer, the optical parameters of which are adjusted by computer settings, and the computer-generated digital fresnel lens profile is superimposed directly onto the phase modulation map.
6. A device for eliminating black grid effect of a phase type spatial light modulator by using a digital Fresnel lens is characterized in that: the device is composed of the following structures: the light source (201) generates incident light waves, and the incident light waves are expanded into parallel light beams after passing through the first lens (202) and the second lens (203); the parallel light beams are transformed into linearly polarized light through a polarizer (204), the linearly polarized light passes through spatial light modulators (205, 210), the spatial light modulators perform phase modulation on the linearly polarized light, the modulated light beams pass through an analyzer (206) and enter an image detector (207), and imaging of the modulated light beams is detected by the image detector (207); the central processing unit (208) receives an input phase modulation graph and superposes a digital Fresnel lens on the phase modulation graph, the convergence effect of the Fresnel lens is utilized to separate the imaging position of the diffraction image of the phase modulation graph from the imaging position of the diffraction image of the black grating, the imaging is received at the position of the diffraction image of the phase modulation graph superposed with the digital Fresnel lens, the light wave diffracted by the black grating is spread at the position, only uniform background light is formed, the background of the received diffraction image is bright, and therefore the influence of the black grating effect on the phase modulation graph of the digital Fresnel lens is eliminated.
7. The apparatus for removing the black-grid effect of a phase type spatial light modulator according to claim 6, wherein: the digital fresnel lens described above is produced by a computer, the optical parameters of which can all be adjusted by computer settings, and the computer-generated digital fresnel lens profile is superimposed directly onto the phase modulation map.
8. The apparatus for removing the black-grid effect of a phase type spatial light modulator according to claim 6, wherein: the diffraction imaging of the phase modulation diagram on the focal plane is completed by utilizing the action of the digital Fresnel lens without using a Fourier lens.
9. The apparatus for removing the black-grid effect of a phase type spatial light modulator according to claim 6, wherein: the spatial light modulator described above is a transmissive spatial light modulator.
10. The apparatus for removing the black-grid effect of a phase type spatial light modulator according to claim 6, wherein: the spatial light modulator described above is a reflective spatial light modulator.
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