CN101799590A - Digital Fresnel method and device for eliminating black-matrix effect of phase spatial light modulator (PSLM) - Google Patents

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

A digital Fresnel method and device for eliminating the black grid effect of a phase-type spatial light modulator

technical field

The invention relates to a method for eliminating the black grid effect of a phase-type spatial light modulator, which belongs to the optical information processing technology.

Background technique

A spatial light modulator (Spatial Light Modulator, SLM) is a device that can modulate a certain parameter of a light wave under the control of a signal source, such as modulating the amplitude through absorption, modulating the phase through the refractive index, and through the rotation of the polarization plane. Modulate the polarization state, etc. It effectively utilizes the parallel, interconnected and high-speed processing capabilities of light, enabling it to spatially modulate light beams in real time, becoming the core component of real-time optical information processing systems, and playing an increasingly important role in the field of modern optics It is the basic component and key device in the research of optical and photoelectric hybrid systems for optical interconnection, optical correlation, optical computing, pattern recognition, optical control, optical detection, image processing, and display technology.

According to the modulation method of SLM, it is mainly divided into two types, one is the amplitude modulation type, and the other is the phase modulation type. Amplitude modulation SLM modulates the amplitude of the incident light wave through the transformation of its transmittance or reflectance, and is mainly used in optical switching, filtering and optical related applications. The reason why SLM has been paid more and more attention to in optical information processing and has been widely used is mainly because it can realize phase modulation. It can change the intensity change of the image into the refractive index change of SLM, thereby modulating the phase. . In this way, the phase that cannot be directly characterized by intensity can be used as an intensity image to achieve phase modulation through SLM. Therefore, a wide range of optical information processing systems, especially some of the latest technologies, such as computational holography, diffractive optical elements, beam shaping, optical tweezers, etc., use phase-type spatial light modulation.

A spatial light modulator is usually composed of a single discrete pixel, and the change of each pixel can be independently controlled, thereby realizing the modulation of the light wavefront in units of pixels. A digital image of the modulated light wave is written to the SLM, and the SLM displays the image. As the incident light wave passes through the SLM, it is spatially modulated. However, since each pixel needs to be surrounded by electrodes, criss-cross opaque regions will be formed on the SLM, so that the device is arranged in a two-dimensional periodic grid structure. Diffraction of light waves by this two-dimensional grating structure will cause two problems: the central bright spot and multi-level diffraction images, especially the central bright spot, whose intensity is much higher than other diffraction orders due to the high concentration of energy. This phenomenon is called the "black grid effect" of the spatial light modulator.

The "black grid effect" is a phenomenon inherent in SLM, which exists even when no image is written to the SLM, and when a modulated image is written, the center of the diffraction image of the written image coincides with the central bright spot , the center of its advanced diffraction image will also coincide with the advanced 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-level diffraction bright spot of the spatial light modulator and cannot be separated , resulting in a serious decline in the quality of the diffraction image, or even unusable. This effect affects the application of the spatial light modulator, and brings extremely adverse effects to the application of the spatial light modulator, which greatly restricts the application of the spatial light modulator in optical information processing.

Therefore, finding a method that can suppress the black grid effect is of great value for the application of spatial light modulators in optical information processing.

Contents of the invention

The purpose of the present invention is to provide a method capable of eliminating the black grid effect of a phase-type spatial light modulator, and the method improves the phase modulation performance of the spatial light modulator.

The present invention is achieved through the following technical scheme: it superimposes a digital Fresnel lens on the phase modulation diagram, and utilizes the converging effect of the Fresnel lens to make the imaging position of the diffraction image of the phase modulation diagram and the diffraction image of the black grid occur Separation, to overcome the black grid effect of the spatial light modulator, is characterized in that it includes the following process: the incident light wave is converted into linearly polarized light by the polarizer, and the linearly polarized light is incident on the light-receiving surface of the spatial light modulator, and the spatial light modulation When the optical modulator works in the state of phase modulation, an analyzer is placed behind the spatial light modulator, and the angle between the polarization axes of the polarizer and the analyzer is adjusted to make the spatial light modulator work in the state of phase modulation, and after the inspection The light intensity transmitted by the polarizer does not change with the degree of phase modulation; a digital Fresnel lens is superimposed on the phase modulation diagram used to modulate the incident light wave, and the superimposed phase modulation diagram is written into the spatial light modulator, and the light wave Refracted by the Fresnel lens, the diffraction image corresponding to the phase modulation pattern can be received on the focal plane of the Fresnel lens, and the focal length of the digital Fresnel lens can be adjusted to receive and observe the diffraction imaging results of the phase modulation pattern at different positions ; The two-dimensional periodic grid structure of the spatial light modulator is not affected by any digital operations, and at the focal plane position of the added digital Fresnel lens, no "black grid effect" is formed, and the light waves diffracted by the black grid Propagated here, according to the effect of Fresnel diffraction, only a uniform background light is formed, so that the background of the received diffraction image is brighter, so that the diffraction image of the phase modulation pattern and the diffraction image of the black grid are in the direction along the optical axis Completely separated to eliminate the influence of "black grid effect" and improve the modulation performance of the spatial light modulator.

Before the phase modulation map is written into the SLM, a digital Fresnel lens generated by computer calculation is superimposed on it, and the result of diffraction imaging is observed on the focal plane of the added Fresnel lens. Due to the converging effect of the Fresnel lens, the diffraction image corresponding to the phase modulation pattern is imaged on its focal plane. Grid effect", that is, the central bright spot and high-level diffraction image have not yet formed. The effect of the black grid is only to form a relatively uniform background light, which will only affect the ratio of the diffraction image of the phase diagram. The disadvantages it brings The effect is much smaller than the central bright spot.

A device for eliminating the black grid effect of a phase-type spatial light modulator by using a digital Fresnel lens, characterized in that the device is composed of the following structure: a light source (201) generates incident light waves, and the incident light waves pass through the first lens (202), After the second lens (203), the incident light wave is expanded into a parallel beam; the parallel beam is converted into linearly polarized light through a polarizer (204), and the linearly polarized light passes through a transmission type spatial light modulator (205), and the spatial light The modulator performs phase modulation on the linearly polarized light, and the modulated light beam passes through the analyzer (206) and is incident on the image detector (207), and its imaging is detected by the image detector (207); the central processing unit (208) receives The phase modulation image is input and a digital Fresnel lens is superimposed on the phase modulation image. Using the converging effect of the Fresnel lens, the diffraction image of the phase modulation image is separated from the imaging position of the diffraction image of the black grid, and the digital Fresnel lens is superimposed. The diffraction image position of the phase modulation pattern of the ear lens is received and imaged, and the light wave diffracted by the black grid propagates at this position, forming only a uniform background light, which makes the background of the received diffraction image brighter, thereby eliminating the "black grid effect" Influence.

The digital Fresnel lens has no effect on the two-dimensional periodic structure of the SLM, and the "black grid effect" will still exist, but the "black grid effect" is the result of Fraunhofer diffraction of the inherent two-dimensional periodic structure of the SLM , so on the focal plane of the Fresnel lens, the "black grid effect" has not yet formed, and the light waves diffracted by the black grid will only form a relatively uniform background light when it propagates to this position, making the background of the received diffraction image relatively Brightness reduces the image contrast, but its adverse effect is much smaller than the central bright spot caused by the black grid effect, so this method overcomes the "black grid effect" of the spatial light modulator very well.

The above-mentioned spatial light modulator can be a transmission type or a reflection type. If it is a reflection type SLM, a beam splitting prism can be used to make the SLM work in the state of normal incidence. The working state of normal incidence is not a necessary condition, the purpose is only to form a coaxial optical system for easy adjustment.

The above-mentioned digital Fresnel lens is generated by a computer, which can easily change the optical parameters such as the focal length according to the design requirements of the actual optical system. After the computer is generated, it can be directly superimposed on the phase modulation diagram.

Compared with existing inventions and technologies, the present invention has the following advantages:

It superposes a digital Fresnel lens on the phase modulation map, and utilizes the converging effect of the Fresnel lens to separate the diffraction image corresponding to the phase modulation map from the diffraction image corresponding to the black grid of the spatial light modulator in the direction of the optical axis. , thereby eliminating the "black grid effect" of the phase-type spatial light modulator. The digital Fresnel lens used in this technology is generated by computer calculation and superimposed on the phase modulation map. This process is completely automatically completed by the computer, and the optical parameters such as the size and focal length of the lens are changed in the digital domain, and are completed by the computer through setting. While eliminating the black grid effect of the phase-type spatial light modulator, no additional devices such as Fourier lenses or filters are needed, and the structure is simple.

Description of drawings

Fig. 1 Schematic diagram of the physical structure of the spatial light modulator. The white area represents the transparent part, and the black area represents the opaque part.

Figure 2 is a schematic diagram of the principle of digital Fresnel eliminating black grid effect.

Fig. 3 Comparison curve of Fresnel diffraction and Fraunhofer diffraction intensity of spatial light modulator. 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 working principle of the transmissive spatial light modulator.

Fig. 5 is a schematic diagram of the working principle of the reflective spatial light modulator.

Figure 6 is the diffraction imaging result before the spatial light modulator is added to the digital Fresnel lens.

Fig. 7 is the diffraction imaging result after the spatial light modulator is added with a digital Fresnel lens.

Fig. 8 is an embodiment of a spatial light modulator after digital Fresnel lenses with different focal lengths are added.

101 in the figure is the initial phase modulation diagram, 102 is the corresponding diffraction image under ideal conditions, 103 is the diffraction image under the influence of the black grid effect of the spatial light modulator, 104 is the digital Fresnel lens, and 105 is the digital Fresnel lens. Diffraction image behind a Neel lens.

In the figure, 201 is a light source, 202 is lens one, 203 is lens two, 204 is a polarizer, 205 is a transmission spatial light modulator, 206 is an analyzer, 207 is an image detector, 208 is a central processing unit, 209 is a beam splitting prism, and 210 is a reflective spatial light modulator.

Detailed ways

The implementation of the technical solution will be further described in detail below in conjunction with the accompanying drawings.

Attached Figure 1 is a schematic diagram of the physical structure of the spatial light modulator. The white area represents the light-transmitting part, which also represents each pixel; the black area represents the opaque part. This inherent physical structure makes the SLM present a two-dimensional grid Structure. The influence of the black grid effect of SLM is mainly in the Fraunhofer diffraction area, so the black grid effect can be regarded as the Fraunhofer diffraction of the two-dimensional grid, and its Fraunhofer diffraction on the Fourier spectrum plane of the focal length of the lens The Fei diffraction field can be regarded as the Fourier transform of the rectangular hole array.

整个M行N列的SLM的透射率函数为

黑栅的透射率函数T(f_x，f_y)：Define the row direction coordinates on the SLM as f _x , the column direction coordinates as f _y , w is the distance between the pixel centers of the SLM, w ₀ is the pixel opening width of the SLM, and the transmittance function of each pixel is

The transmittance function of the SLM with M rows and N columns is

The transmittance function T(f _x , f _y ) of the black grid:

$\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; mw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; comb</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

Under the irradiation of plane wave U ₀ (f _x , f _y ), the complex amplitude distribution obtained by multiplying the plane wave and black grid transmittance function is:

$\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; comb</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; jkz</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The Fraunhofer diffraction pattern on the Fourier spectrum plane is:

$\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; o</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

in,

$\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; T</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; mw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; nw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; rect</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span>\mathrm{<span\; class="notranslate">\; comb</span>}<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">f</figure-callout></span><figure-callout\; id="0"\; label="f\; x\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}}{{}_{}}<span\; class="notranslate">\; ,</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="MN\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">MN</figure-callout></span><figure-callout\; id="0"\; label="MN\; w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}_{}^{}{\mathrm{<span\; class="notranslate">w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; mw</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="nw"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">nw</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; wx</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; sin</span>}\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; wy</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&times;</span>\mathrm{<span\; class="notranslate">\; comb</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; comb</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="w"\; filenames="HSA00000048630100013.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>$

Through the theoretical derivation of formulas (1)-(4), the two-dimensional grid on the SLM has convolution modulation on the Fraunhofer diffraction pattern of the incident plane wave on the Fourier spectrum plane. This is determined by the physical structure of the SLM, regardless of any input information, this effect will exist. But since the black grid effect is the result of Fraunhofer diffraction, if it is observed or received in the near field, the phase modulation pattern and the diffraction image of the black grid will propagate for a certain distance in the form of Fresnel diffraction. A digital Fresnel lens is superimposed on the phase modulation diagram of the phase modulation diagram, and the diffraction image corresponding to the phase modulation diagram will be observed on its focal plane, and the black grid effect has not yet formed at this time. Therefore, a schematic diagram of a method for eliminating the SLM black grid effect by using a digital Fresnel lens is shown in Figure 2.

Figure 2 is a schematic diagram of the principle of eliminating the black grid effect through phase compensation. The diffraction imaging result corresponding to the phase modulation diagram 101 under ideal conditions is shown in 102. After the phase modulation diagram 101 is written into the spatial light modulators 205 and 210, due to the black grid effect of the spatial light modulators 205 and 210, this The result of time-diffraction imaging is shown in 103, as shown in the figure, the black grid effect causes the central bright spot and the high-level diffraction image to be coupled together with the effective optical information and cannot be separated. In the present invention, before the phase modulation diagram 101 is written into the spatial light modulators 205 and 210, a digital Fresnel lens 104 is first superimposed, and at this time the field distribution of the diffraction image on the back focal plane of the lens is U′ _f (x, y) is :

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}}{\mathrm{<span\; class="notranslate">\; j\&lambda;f</span>}}\underset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dx</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; dy</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Where U(x ₁ , y ₁ ) is the input phase modulation map, (x ₁ , y ₁ ) is the input plane coordinates, (x, y) is the output plane coordinates, λ is the wavelength, and f is the focal length. It can be seen from formula (5) that the field distribution at the focal plane is the Fraunhofer diffraction pattern of the field incident on the Fresnel lens. At this time, the field distribution of the black grid on the back focal plane of the Fresnel lens is U _f ″(x, y):

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; \&prime;</span><span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; jf</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}}}{\mathrm{<span\; class="notranslate">\; j\&lambda;f</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}\underset{<span\; class="notranslate">\; \&infin;</span>}{<span\; class="notranslate">\; \&Integral;</span><span\; class="notranslate">\; \&Integral;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; dx</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; dy</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

Where U′(x ₁ , y ₁ ) is a function of the spatial light modulator, and it can be known from formula (6) that the field distribution of the black grid at the focal plane of the Fresnel lens is its Fresnel diffraction pattern. As shown in Figure 3, the Fresnel diffraction intensity and its Fraunhofer diffraction intensity of the simulated spatial light modulator on the focal plane of the Fresnel lens are represented as dashed and solid lines, respectively, and are displayed in the same coordinate system Down. From the accompanying drawing 3, it can be seen that the intensity of the diffraction field at the focal plane of the Fresnel lens is much smaller than that of Fraunhofer diffraction, and it can be approximated that the light intensity distribution is uniform, which is the observation or receiving surface. A background light intensity on the above, the effect at this time is shown as 105 in the accompanying drawing 2, the background of the received image is brighter, but there will be no serious central bright spot problem.

The phase factor of the added digital Fresnel lens is exp[jπ/λf(x ₁ ² +y ₁ ² )], which is used as the phase compensation template 104 and multiplied by the phase factor corresponding to the original phase modulation diagram 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 focal length must ensure that the diffraction of the two-dimensional grid of the spatial light modulator satisfies the approximate conditions of Fresnel diffraction, that is, it cannot be close to Fraunhofer due to too large a focal length. 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 the decrease of the focal length, and if the focal length is too small, the sampling theorem will not be satisfied.

First consider the propagation distance. When Fresnel diffraction is established, f needs to satisfy:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ></span><span\; class="notranslate">\; ></span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

The approximate conditions for Fraunhofer diffraction are:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; h</span>}}<span\; class="notranslate">\; ></span><span\; class="notranslate">\; ></span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

Then the value range of the focal length should be between f _n and f _h . From the consideration of satisfying the sampling theorem, if the sampling interval (or pixel size) of the spatial light modulator is d and the number of pixels is N×N, then the maximum spatial frequency of the Fresnel lens function on the spatial light modulator is:

${\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; Nd</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;\; f</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 9</span>}<span\; class="notranslate">\; )</span>$

According to the sampling theorem, the sampling interval must be smaller than the reciprocal of the maximum spatial frequency of the sampling function, that is, d≤1/ε _max , thus the restriction on the focal length of the lens is obtained as follows:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; \&Greater\; Equal;</span>\frac{{\mathrm{<span\; class="notranslate">\; Nd</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 10</span>}<span\; class="notranslate">\; )</span>$

Therefore, the maximum value of the focal length of the digital Fresnel lens should be less than f _h , and the minimum value should be selected from the larger of f _n and f _c .

According to the above method, the system for realizing the suppression of the black grid effect of the phase-type spatial light modulator mainly includes a light source, a spatial light modulator, a polarizer and an analyzer, a spatial filter, an image detector and a central processing unit. Said light source can be a coherent light source or a partially coherent light source; said spatial light modulator can be reflective or transmissive; said polarizer and analyzer are a pair of polarizing devices, the main function of which is Ensure 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 a combination of a digital signal processor and a programmable application-specific integrated circuit, which can be a computer or a is an embedded system. It is characterized in that the phase modulation diagram generated by the calculation of the central processing unit is superimposed on the digital Fresnel lens and written into the spatial light modulator, and diffraction occurs under the irradiation of the incident light wave, and the image is displayed on the focal plane corresponding to the digital Fresnel lens The detector receives, and then the central processing unit stores and displays the imaging results.

The embodiment will be further described below in conjunction with the accompanying drawings.

Figure 4 is a schematic diagram of the working principle of the transmissive spatial light modulator. As shown in the figure, the light wave output by the light source 201 is expanded and collimated by the beam expander and collimation system composed of the first lens 202 and the second lens 203, and passes through the polarizer 204 so that the light wave enters the transmissive spatial light modulator 205 as linearly polarized light. After the light wave passes through the transmission-type spatial light modulation 205, it passes through a polarizer 206. The functions of the polarizer 204 and the polarizer 206 are to ensure that the incident light wave is linearly polarized light, and the transmission-type spatial light modulator 205 works in phase modulation state. The central processing unit 208 calculates and generates or writes the stored phase modulation map into the transmissive spatial light modulator 205 after being superimposed on the digital Fresnel lens, and receives and displays the diffraction imaging result transmitted by the image detector 207 .

Figure 5 is a schematic diagram of the working principle of the reflective spatial light modulator. As shown in the figure, the light wave output by the light source 201 is beam expanded and collimated by the beam expander and collimation system composed of 202 lens 1 and 203 lens 2, and the light wave is split into two beams after entering the beam splitting prism 209 with linear polarization through the polarizer 204 , wherein the transmitted light beam is modulated and reflected by the reflective spatial light modulator 210 , and then reflected by the beam splitting prism 209 , and enters the analyzer 206 . The central processing unit 208 calculates and generates or writes the stored phase modulation map into the reflective spatial light modulator 210 after being superimposed on the digital Fresnel lens, and receives and displays the diffraction imaging result transmitted by the image detector 207 .

Figure 6 is the diffraction imaging result before the spatial light modulator is added to the digital Fresnel lens. Where (a) is the original image, (b) is the phase diagram of the diffractive optical element corresponding to the calculated image (a), (c) is the result of diffraction imaging after the image (b) is directly written into the SLM, due to the black grid effect The presence of a central bright spot is clearly visible.

Accompanying drawing 7 is the diffraction imaging result after the spatial light modulator is added with a digital Fresnel lens. Among them, (a) is the image after superimposing the digital Fresnel lens on the accompanying drawing 6 (b), (b) is the result of diffraction imaging after the image in (a) is written into the SLM, it is obvious that the bright spot in the center has been eliminated, and the black grid The effect is only to make the background of the image brighter, and compared with Fig. 6(c), the modulation performance of the spatial light modulator is significantly improved.

Figure 8 is the result of adding digital Fresnel lenses with different focal lengths to the spatial light modulator. The size of the added digital Fresnel lens is 512×512 pixels, the pixel interval d is 19 μm, and the light wavelength of the laser is 532nm. According to formulas (7) to (10), the calculated focal length f ranges from 0.2 to 45m , this is the scope of application of theoretical calculations. Combined with actual use, the typical value generally needs to be greater than the minimum value, and it is convenient for observation or imaging. If the focal length is too large, the "black grid effect" will increase as the diffraction distance increases. "Gradually enhanced, affecting image quality. In the embodiment, the focal lengths f are taken as 300mm, 350mm, 400mm, 450mm, and 500mm respectively, corresponding to figures (a), (b), (c), (d), and (e) respectively. Observing the reproduced image on its focal plane, it can be seen from the figure that since the Fourier lens is not used in the present invention, the black grid phenomenon can only be formed by Fraunhofer far-field diffraction, for digital Fresnel with different focal lengths The imaging results corresponding to the ear lens and the phase modulation diagram are very clear.

Claims (10)

1. A method for eliminating the black grid effect of a phase-type spatial light modulator, characterized in that: by superimposing a digital Fresnel lens on the phase modulation figure, utilizing the aggregation of the Fresnel lens to make the diffraction image of the phase modulation figure and The imaging position of the diffraction image of the black grid is separated to overcome the black grid effect of the spatial light modulator, which is characterized in that it includes the following process: the incident light wave is converted into linearly polarized light by the polarizer, and the linearly polarized light is incident on the spatial light modulator The light-receiving surface, the spatial light modulator works in the state of phase modulation, an analyzer is placed behind the spatial light modulator, and the angle between the polarization axes of the polarizer and the analyzer is adjusted to make the spatial light modulator work at Phase modulation state, and the light intensity transmitted by the analyzer does not change with the degree of phase modulation; a digital Fresnel lens is superimposed on the phase modulation diagram used to modulate the incident light wave, and the superimposed phase modulation diagram is written The light waves are collected by the digital Fresnel lens, and the diffraction image corresponding to the phase modulation pattern can be received on the focal plane of the Fresnel lens, and the focal length of the digital Fresnel lens can be adjusted to receive observations at different positions The result of diffraction imaging of the phase modulation diagram; the two-dimensional periodic grid structure of the spatial light modulator is not affected by digital operations, and the "black grid effect" has not yet been formed at the focal plane position of the added digital Fresnel lens ”, the light wave diffracted by the two-dimensional grating propagates to this position, because the effect of Fresnel diffraction only forms a uniform background light, which makes the background of the received diffraction image brighter, so that the diffraction image of the phase modulation pattern is different from the black The diffraction image of the grating is completely separated along the optical axis to eliminate the influence of the "black grating effect" and improve the modulation performance of the spatial light modulator. 2. the method for eliminating the black grid effect of phase type spatial light modulator as claimed in claim 1 is characterized in that: utilize the effect of digital Fresnel lens self, complete the diffraction imaging of phase modulation figure on the focal plane, without Use an additional Fourier lens. 3. The method for eliminating the black grid effect of a phase-type spatial light modulator according to claim 1, wherein the above-mentioned spatial light modulator is a transmissive spatial light modulator. 4. The method for eliminating the black grid effect of a phase-type spatial light modulator according to claim 1, wherein the above-mentioned spatial light modulator is a reflective spatial light modulator. 5. the method for eliminating phase-type spatial light modulator black grid effect as claimed in claim 1, is characterized in that: above-mentioned digital Fresnel lens is produced by computer, and its optical parameter is all set and adjusted by computer, and the computer-generated The digital Fresnel lens profile is superimposed directly onto the phase modulation map. 6. A device utilizing a digital Fresnel lens to eliminate the black grid effect of a phase-type spatial light modulator, characterized in that: the device is composed of the following structure: a light source (201) generates incident light waves, and the incident light waves pass through the first lens (202 ), after the second lens (203), the incident light wave is expanded into a parallel beam; the parallel beam is transformed into linearly polarized light through a polarizer (204), and the linearly polarized light passes through a spatial light modulator (205, 210), the The spatial light modulator performs phase modulation on the linearly polarized light, the modulated light beam passes through the analyzer (206), and is incident on the image detector (207), and its imaging is detected by the image detector (207); the central processing unit (208 ) receives the input phase modulation image and superimposes a digital Fresnel lens on the phase modulation image, using the converging effect of the Fresnel lens to separate the imaging position of the diffraction image of the phase modulation image from the imaging position of the black grating, and the superimposed The position of the diffraction image of the phase modulation pattern of the digital Fresnel lens is received and imaged, and the light wave diffracted by the black grid propagates at this position, forming only a uniform background light, which makes the background of the received diffraction image brighter, thereby eliminating the "black The influence of grating effect on the phase modulation diagram of digital Fresnel lens. 7. the device utilizing digital Fresnel lens to eliminate phase-type spatial light modulator black grating effect as claimed in claim 6, is characterized in that: above-mentioned digital Fresnel lens is produced by computer, and its optical parameter all can be by The computer settings are adjusted and the computer-generated digital Fresnel lens profile is superimposed directly onto the phase modulation map. 8. The device for eliminating the black grid effect of a phase-type spatial light modulator as claimed in claim 6, characterized in that: utilize the effect of a digital Fresnel lens to complete the diffraction imaging of the phase modulation diagram on the focal plane without using Fourier Lie lens. 9. The device for eliminating the black grid effect of a phase-type spatial light modulator according to claim 6, wherein the above-mentioned spatial light modulator is a transmissive spatial light modulator. 10. The device for eliminating the black grid effect of a phase-type spatial light modulator according to claim 6, wherein the above-mentioned spatial light modulator is a reflective spatial light modulator.

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