CN108732669B

CN108732669B - Global random coding binary diffraction grating

Info

Publication number: CN108732669B
Application number: CN201810527073.4A
Authority: CN
Inventors: 刘克; 王健年; 李艳秋
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2018-05-29
Filing date: 2018-05-29
Publication date: 2021-04-06
Anticipated expiration: 2038-05-29
Also published as: CN108732669A

Abstract

The invention discloses a global random coding binarization diffraction grating, which is characterized in that two transmissivity pixels are adopted to carry out global random distribution on the diffraction grating, and the average transmissivity of the same pixel position in each period is ensured to be equal to the transmissivity of any ideal diffraction grating at the corresponding position; the global random coding binarization diffraction grating has a diffraction light field similar to an ideal grating: the light amplitude at the diffraction order is equal and only negligible noise light is present at the non-diffraction order. The diffraction grating can completely eliminate high-order diffracted light without an order selection plate when being applied to a four-beam transverse shearing interference technology, avoids the loss of precision and a measurement range, has better effect of inhibiting high-order diffraction order secondary light compared with an improved Hartmann mask or a random coding mixed grating, and improves the detection precision of wavefront.

Description

Global random coding binary diffraction grating

Technical Field

The invention belongs to the technical field of diffraction gratings, and particularly relates to a global random coding binarization diffraction grating.

Background

The transverse shearing interference technology refers to that the wave front emitted by a detected optical element or system is copied into a plurality of shearing wave surfaces through a light splitting element, and a certain transverse dislocation quantity (shearing quantity) is generated, so that shearing wave surface information along the shearing direction can be acquired in an interference pattern of an overlapping region of light waves, and the purpose of measuring the phase distribution of the wave front is achieved. The shearing interference technology belongs to common-path interference, has low requirement on the stability of a measuring environment, has no special requirement on the coherence of a light source and the like, and is generally not limited by the caliber. Based on the above characteristics, the transverse shearing interference technology is widely applied in the detection of optical systems and optical devices, the research of liquid and gas flow, the stress, strain and vibration analysis in experimental mechanics, and the like.

The grating-based four-wave plane lateral shear interference technology is the mainstream of the lateral shear interference technology at present. The most significant problem encountered in grating lateral shear interference techniques arises from the inevitable presence of unwanted higher order diffraction orders in the diffraction field of the grating, which orders mean unwanted shear wave surfaces, the introduction of which will introduce measurement errors.

To suppress higher diffraction orders, the prior art is roughly divided into two categories: unnecessary high-order diffraction orders are filtered by using a level selection plate in a spatial filtering system, and the defects that the existence of the level selection plate causes the complex adjustment structure of the system, the requirement on the precision of an instrument adjustment mechanism is high, the adjustment difficulty is large, the size of the level selection plate can influence the measurable wavefront distortion range, and the precision of transient wavefront detection is reduced; the improved transverse shearing interference optical splitting element is represented by an improved Hartmann mask transverse shearing interference technology and a random coding mixed grating transverse shearing interference technology. Namely, by designing the structure of the grating, the redundant diffraction orders in the diffraction field of the grating are directly inhibited, thereby simplifying the system structure. The transmittance distribution of an ideal grating required for four-wave-plane lateral shear interference should be a two-dimensional sinusoidal distribution of between ± 1, however, it is extremely difficult to process such an ideal grating in practical applications. As an approximate alternative to an ideal sinusoidal grating, either a modified Hartmann mask or a randomly coded hybrid grating, introduces higher diffraction orders, which also affects the lateral shear interference between the + -1 orders. Therefore, it is necessary to design a new grating for suppressing all diffraction orders except for the necessary diffraction order and further improving the detection accuracy.

Disclosure of Invention

In view of this, the present invention aims to provide a global random coding binary diffraction grating, which has a diffraction light field similar to that of any ideal grating and can reduce the processing difficulty of the grating. Wherein, the transmissivity function of the ideal diffraction grating can be set according to actual requirements.

The invention relates to a global random coding binaryzation diffraction grating, wherein each period of the diffraction grating consists of a plurality of pixels;

the pixels have two different set transmittances, and the two transmittance pixels are randomly distributed on the diffraction grating and satisfy: for the same pixel position of each period, the average transmittance of the pixel position is equal to the transmittance of the ideal diffraction grating at the corresponding position.

Preferably, the period width is greater than or equal to the width of 5 picture elements.

Preferably, the two different set transmittances are 1 and-1, respectively.

Preferably, the two different set transmittances are 1 and 0, respectively.

Preferably, the two different set transmittances are 0 and-1, respectively.

The invention has the following beneficial effects:

the invention provides a global random coding binarization diffraction grating, which is characterized in that two transmissivity pixels are adopted to carry out global random distribution on the diffraction grating, and the average transmissivity of the same pixel position in each period is ensured to be equal to the transmissivity of any ideal diffraction grating at the corresponding position; the global random coding binarization diffraction grating has a diffraction light field similar to an ideal grating, the light amplitude at the diffraction order is equal, and only negligible noise exists at the non-diffraction order. The global random coding binary diffraction grating has only two kinds of transmissivity and can be used as an approximate substitute of an ideal grating which is difficult to process. The diffraction grating can completely eliminate high-order diffracted light without an order selection plate when being applied to a four-beam transverse shearing interference technology, thereby avoiding the loss of precision and measurement range, and simultaneously compared with an improved Hartmann mask or a random coding mixed grating, the diffraction grating has better effect of inhibiting high-order diffraction order secondary light and improves the detection precision of wave front; in addition, because the image elements in the grating have only two transmittances, the grating structure has the advantage of being easier to process.

Drawings

Fig. 1(a) is an equivalent function corresponding to a grating in the case where S is equal to 6 μm by 6 μm, fig. 1(b) is an equivalent function corresponding to a grating in the case where S is equal to 4 μm by 4 μm, and fig. 1(c) is an ideal sinusoidal function;

FIG. 1(d) is an equivalent function of a globally randomly encoded grating when the ideal grating is a sinusoidal grating;

FIG. 2 is a transmittance distribution of one period of a two-dimensional sinusoidal grating;

FIG. 3 is a graph showing transmittance distribution at the same pixel position over all periods of a phase diffraction grating;

FIG. 4 is a schematic diagram of the distribution of etched regions of a global random coded phase grating in a 240 μm by 240 μm region;

FIG. 5 is a one-dimensional amplitude normalized contrast plot of the diffracted light field of the global random encoded diffraction grating of the present invention and the diffracted light field of an ideal two-dimensional sinusoidal grating.

Detailed Description

The invention is described in detail below by way of example with reference to the accompanying drawings.

In some applications, the fabrication of an ideal grating with continuous transmission variation is difficult. The design of the original random coding mixed grating based on the light flux constraint shows that a certain grating formed by randomly distributing easily-processed pixels reasonably designs the constraint condition of random distribution of the certain grating, so that the diffraction light field of the grating can be close to the diffraction light field of an ideal grating.

The random coding mixed grating based on the light flux constraint is used as an approximate substitute of an ideal sinusoidal grating and applied to a four-beam transverse shearing interference technology. The encoding principle based on the luminous flux constraint is as follows: the grating of one period is equally divided into square areas with the area S, each square area contains pixels with different transmittances as the minimum unit, the pixels are randomly distributed under the condition that the total luminous flux of the pixels in the square meets the distribution of an ideal function, the step is repeated for each period to complete the structure of the random coding amplitude grating, and then a chessboard phase grating with the period twice as large is combined to complete the structure of the random coding mixed grating.

The spatial spectrum of the grating can be obtained by performing fourier transform on the transmission function of the grating, and the spectral value at (k/d, k '/d) in the spatial spectrum, i.e. the amplitude of the diffracted light of the (k, k') order, where d is the width of the grating period. Due to the random distribution of the image elements, the transmission functions of different random encoding gratings are different, but the spectral values at (k/d, k '/d) in the spatial frequency spectrums, namely the amplitudes of the (k, k') orders of diffracted light, are the same.

Setting the number of cycles contained in the grating as N × N, the number of pixels contained in a single cycle of the grating as D × D, setting the size of the pixels as w × w, and taking the upper left corner of the grating as the origin of (x, y), the transmission function of the whole grating is regarded as that each two-dimensional window function in the first cycle of the upper left corner is respectively convolved with the pulse functions delta (x-aDw, y-bDw) under different cycles:

where m, n represents the pixel in the mth row and nth column of the cycle, H_mnabFor the high of the impulse function, i.e. the transmittance of the picture elements, m, n, a, b represent that the impulse function is located at the picture elements of the mth row and nth column in the period of the ath row and the kth column on the grating.

Fourier transforming the transmission function to obtain the amplitude density at (k/d, k '/d) in the space frequency spectrum of the grating, wherein k, k' ∈ Z:

wherein F_u,v{. is the Fourier transform operator, the subscripts u, v denote the values of the transformed spectral coordinates, and S_mnIs the sum of the transmittances of the picture elements of the mth row and the nth column in different periods.

The function distribution in the above Fourier transform symbols is called the equivalent function, which is height S_mnThe width of the window function, i.e. the width of the picture element. The equivalent function is Fourier transformed, and the spectral value at (k/d, k '/d) is the spectral value at (k/d, k '/d) in the spatial spectrum of the randomly encoded grating, i.e., the amplitude of the (k, k ') order diffracted light of the grating.

In the random coding mixed grating, the grating period size is 120 μm × 120 μm, the pixel size is 2 μm × 2 μm, fig. 1(a) is an equivalent function corresponding to the grating when S is equal to 6 μm × 6 μm, fig. 1(b) is an equivalent function corresponding to the grating when S is equal to 4 μm × 4 μm, and fig. 1(c) is an ideal sine function. It can be seen that the values of the equivalent functions in the square region S are all equal due to the restriction of the luminous flux, so that the equivalent function of the grating is greatly different from the ideal sinusoidal function, and thus the diffracted light field of the grating is greatly different from that of the ideal sinusoidal grating.

Subject to the luminous flux constraint, the equivalent functions in the square regions S in the randomly coded hybrid grating all have equal values. Then, the coding mode is modified to make the m-th in different periodsSum S of transmittances of picture elements of row n column_mnEqual to the sum of the transmittances of the ideal grating at that location, the equivalent function of the grating can then approach the transmission function of the ideal grating.

Taking the ideal grating as a sinusoidal grating as an example, the number of pixels contained in a single period of the grating D x D is set to 40 x 40, and the equivalent function at this time is shown in fig. 2, which can already approach the transmission function of the ideal sinusoidal grating. It is readily found that the equivalent function is closer to a sinusoidal function as the width w of the pixel is smaller. The randomly coded grating and the sinusoidal grating now have approximately equal spectral values at the diffraction orders in the spatial spectrum.

The average value of the transmissivity of the image element of the mth row and the nth column in each period is equal to the transmissivity of the ideal grating transmission function at the image element, which is the improved encoding constraint rule of the random encoding grating. It is noted that the constraint rule is independent of the specific form of the transmission function of the ideal grating and is therefore applicable to approximate replacement of any ideal grating. Under the condition that the pixels of the random coding grating meet the constraint, the pixels are distributed on the whole grating globally and randomly so as to inhibit the spectrum value at the non-diffraction order, and the random coding grating which is approximately equal to the spectrum value of any ideal grating at the diffraction order, namely the diffraction light field, can be obtained. The pixels of the random coding grating are globally and randomly distributed in different periods, so that the random coding grating is named as the global random coding grating.

In consideration of reducing the processing difficulty, the invention adopts two pixel arrays with different transmittances to form the diffraction grating, so that the two transmittance pixels are randomly distributed on the diffraction grating and meet the following requirements: for the same pixel position of each period, the average transmittance of the pixel position is equal to the transmittance of the ideal diffraction grating at the corresponding position. Wherein, the transmissivity function of the ideal diffraction grating can be set according to actual requirements. As shown in fig. 3, there are two types of transmittance at different periods for the same pixel position, and by this distribution rule, the average transmittance at the pixel position is the transmittance of the ideal diffraction grating at that position.

In a specific implementation, for example, the desired beam splitting element required in a four-beam shearing interferometry is a beam splitter with a transmission between-1 and 1Of a two-dimensional sinusoidal grating having a transmission function of

The distribution of one cycle is shown in fig. 1 (d). In practical application, an optical path is difficult to design and manufacture the grating, but the easily-processed global random coding binarization grating can be adopted to be a good substitute. For convenience of processing, the pixels are square.

A transparent substrate is taken, and the pixels with two different transmittances can be pixels with +1 transmittance and pixels with-1 transmittance. The +1 transmittance may be the transmittance of the light-transmissive substrate itself, while the-1 transmittance is achieved by phase modulating the incident light by etching the depth of the substrate. The etching depth is

Where λ is the wavelength of the incident light wave and n is the refractive index of the substrate.

It is also possible to design a diffraction grating with a pixel transmittance of 1 and 0 or 0 and-1, respectively.

Under the above coding constraint rule, the global random coding binarization grating structure obtained in this embodiment is a transparent substrate with an etched region, as shown in fig. 4, where the material of the substrate is selected from fused silica, the minimum composition unit of the etched region is 2 μm × 2 μm square, and the grating period width d is 240 μm.

The comparison of the diffracted light field of the global random coding binarization grating and the diffracted light field of the ideal two-dimensional sine grating is shown in fig. 5, it can be seen that the global random coding binarization grating is similar to the diffracted light field of the ideal sine grating, only + -1-order diffracted light and negligible noise light exist, wherein k is the order of the diffracted light, and the requirement of the light splitting element in the four-beam transverse shearing interference system is met.

In order to ensure a diffraction light field close to an ideal grating, the period width needs to be greater than or equal to the width of 5 pixels.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A global random coding binary diffraction grating is characterized in that,

each period of the diffraction grating is composed of a plurality of pixels;

2. The global randomly encoded binarized diffraction grating of claim 1, wherein the period width is greater than or equal to the width of 5 pixels.

3. The global randomly encoded binary diffraction grating of claim 1, wherein the two different set transmittances are 1 and-1, respectively.

4. The global randomly encoded binarized diffraction grating of claim 1, wherein said two different set transmittances are 1 and 0, respectively.

5. The global randomly encoded binary diffraction grating of claim 1, wherein the two different set transmittances are 0 and-1, respectively.