CN108955905B - Wavefront sensor based on improved Hartmann mask and detection method - Google Patents
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Abstract
The invention relates to a wavefront sensor based on a circular light-transmitting area improved Hartmann mask and a detection method. The wavefront sensor comprises a diffraction element and a detector, wherein the diffraction element is a mixed grating consisting of a checkerboard phase grating and an amplitude grating with a circular light transmission area, and when the diffraction element is used for four-wavefront shearing interference, the diffraction element has better diffraction spectrum characteristics than an improved Hartmann Mask (MHM) widely used at present, namely higher +/-1-level diffraction efficiency, so that the system error in the differential wavefront extraction process is further reduced, and the measurement accuracy is improved; by properly selecting the quantization factor of the amplitude grating, the grating structure can be simplified on the premise of ensuring the diffraction efficiency, and the processing difficulty of components is reduced. The device can be used in the field of high-precision wavefront detection.
Description
Technical Field
The invention belongs to the field of optical wavefront detection, and particularly relates to a shearing interference wavefront sensor based on amplitude and phase mixed gratings and a detection method.
Background
The high-precision wavefront measurement technology is widely applied to the fields of surface shape detection of optical elements, wave aberration measurement of high-resolution optical systems, astronomical observation, quality evaluation of high-energy laser beams, in-vivo imaging of biological tissues and the like.
Shear interference is a typical wavefront interferometry technique without a standard mirror, and interference occurs by superposition of a wavefront to be measured and a shear wavefront after dislocation of the wavefront. Because the required reference wavefront is generated without depending on standard mirrors or pinhole diffraction, compared with the traditional interference technologies such as phase-shifting point diffraction interference and the like, the shearing interference technology can simplify the structure of an optical path and reduce the operation difficulty, has the advantages of large dynamic range, easiness in integration, instrumentization and the like, and is commonly used for testing the surface shape of a large optical element. In addition, since the two beams of light that interfere are nearly aplanatic, shear interference is less affected by air disturbances and mechanical vibrations than conventional interferometric techniques.
The grating shearing interference technology uses the grating as a light splitting element, and has the advantages of simple device structure, low processing difficulty, convenience in system integration and the like. Meanwhile, system errors caused by the use of structures such as prisms, beam splitters and reflectors are avoided, and the overall measurement precision is improved. The grating spectroscopic structure has wide application in lateral shear interference techniques, such as the classical Ronchi test. In 1997, Schreiber et al proposed a lateral shearing interference device based on two Ronchi phase grating structures, which achieves the lateral shearing interference between + -1 st-order diffracted lights (Schreiber, H., and J.Schwider. "laser shearing interferometer based on two Ronchi phase gratings in series." applied optics 36.22(1997): 5321-) -5324.).
However, the conventional transversal shearing interferometry generally needs to perform two measurements in orthogonal directions and then synthesize the two measurements into a final wavefront to be obtained, and the asynchronous exposure process increases the complexity of the measurement process and introduces systematic errors, thereby limiting the precision and the use scene of the technology. Researchers have therefore begun to focus on multi-wavefront lateral shear interference techniques.
In 1993, Primot proposed a Three-wave lateral shearing interference device using prisms for spectroscopic shearing (Primot, Jerometer, "Three-wave shearing interferometer," Applied optics32.31(1993): 6242-6249.). The three beams of copy light are cut and superposed in a mode of forming an angle of 120 degrees with each other, phase gradients in three directions are generated in the same auxiliary interference image, then wave front gradient values in two directions are obtained through a projection method, and finally the wave front to be solved is solved. However, the method has high requirements on the processing precision of the light splitting element, and the measurement precision is limited. In 1995, Primot and Sogno redesign a wave front light splitting scheme on the basis of the previous three-wave transverse shearing interference device, and realize wave front light splitting by adopting a bidirectional hexagonal etching structure grating. The improvement realizes the accuracy of the wave loss direction of the light splitting wave front, and the grating structure can be used as a multi-wave-surface light splitting element.
In 2000, Primot and guerineau proposed an improved Hartmann Mask (MHM) based on the conventional Hartmann method, which improved the diffraction characteristics of the Hartmann Mask by adding a phase grating to concentrate the energy distribution on four diffraction orders participating in interference (Primot J, gurrieau. extended Hartmann test based on the observation of the diffraction characteristics of a Hartmann Mask complex b a phase grating [ J ] Applied optics,2000,39(31): 5715-. The MHM grating structure consists of a checkerboard phase grating and a rectangular amplitude grating, the duty ratio of the amplitude grating is 2/3, and the period of the phase grating is 2 times that of the amplitude grating. Under the condition of central wavelength, diffraction light of multiple orders of even numbers and +/-3 in a diffraction field of the MHM grating structure is eliminated, and only +/-1 order diffraction light exists in +/-4 orders, so that phase information of a wave front to be measured can be obtained without a order selection window. In 2004, Velghe, Primot and Gumerineau used a modified Hartmann mask for multiple beam shearing interference techniques, proposing the concept of four-Wave lateral shearing interference (Velghe, Sabrina, et al. "Wave-front correlation from multidirectional phase interference generated by multiple shearing interference interferometers" Optics letters 30.3(2005): 245-. Experiments show that compared with the traditional two-beam shearing interference, the four-beam shearing interference technology can obtain higher signal-to-noise ratio, thereby improving the measurement precision. The four-wave transverse shearing interference technology has the advantages of compact device, achromatism, large dynamic range, high accuracy and the like. However, the MHM grating structure still retains the high-order diffraction orders of ± 5, ± 7, etc., which affects the interference between the ± 1 st-order diffracted lights in the x and y directions in the actual measurement process, and limits the further improvement of the measurement accuracy.
In 2015, Ling et al proposed a random coded hybrid grating structure based on luminous flux constraints (Ling T, Liu D, Yue X, et al, Quadrive wave linear imaging based on aligned encoded hybrid grating [ J ]. Optics letters,2015,40(10):2245 2248.). The structure restrains the luminous flux of the amplitude grating in a random coding mode on the basis of an MHM grating structure, so that the transmittance function of the amplitude grating approximately meets an ideal cosine half-wave form, all diffraction orders except +/-1 order are eliminated in principle, an approximately ideal four-wave interference model is formed, and the detection precision of the wavefront to be detected is further improved. However, the design of random coding provides challenges for the processing of the amplitude grating, the processing yield is relatively low, and the application scenarios of the random coding mixed grating are limited.
Disclosure of Invention
The invention aims to combine the advantages of the prior art and overcome the defects of the prior art, and provides a wavefront sensor based on an improved Hartmann mask and a detection method. A mixed grating composed of an amplitude grating and a checkerboard phase grating with approximately circular light-transmitting areas is used as a diffraction light splitting element. On one hand, compared with the improved Hartmann mask (MHM) widely adopted at present, the intensity of a high-order diffraction order is further suppressed, and the system error in the differential wavefront extraction process is reduced in principle; on the other hand, compared with a random encoding mixed grating (REHG) with diffraction characteristics close to ideal conditions, the method reduces the difficulty of processing and manufacturing on the premise of ensuring the diffraction efficiency of +/-1 order, thereby having wider application range.
The technical solution of the invention is as follows:
a wave front sensor based on improved Hartmann mask comprises a diffraction optical element and a two-dimensional photoelectric detector, wherein the diffraction optical element is a two-dimensional grating structure with the same period in the orthogonal direction and is formed by mixing an amplitude grating with the period of T and a light transmission area of approximate circle and a chessboard-shaped phase grating with the period of 2T and the phase gradient of pi under the central wavelength; the position relation of the diffraction optical element and the two-dimensional photoelectric detector is as follows: the diffraction optical element and the two-dimensional photoelectric detector are arranged along the transmission direction of the measured wavefront in sequence.
The light-transmitting area is an approximately circular amplitude grating, and the amplitude transmittance of the light-transmitting area under a plane rectangular coordinate system has the following form:
wherein, T is the period of the amplitude grating, circ () is the circular domain function, a is the radius of the circular light-transmitting area of the amplitude grating, and (b) is the dirac delta function.
The light transmission area in each quadrant of the amplitude grating is a non-rectangular figure which is formed by splicing a plurality of rectangles and is approximate to 1/4 circle. The number of rectangles used for splicing in each quadrant is N, N is a quantization factor, and N is more than or equal to 2. The geometric parameters of the rectangle are a series of angles theta formed by the intersection point of the rectangular frame and the circumference and the coordinate axis1,θ2,...θ2NIs uniquely determined and satisfied
Where j is 1, 2.. 2N, iteration starting value
The light-transmitting area is an amplitude grating which is approximately circular, and the radius a of the light-transmitting area is numerically expressed by an equation
The first non-zero root of (1), wherein J1Is a first order class Bessel function.
The amplitude transmittance of the checkerboard phase grating meets the following form:
wherein T is the period of the amplitude grating,
is the amount of phase retardation of the phase grating under illumination of the center wavelength,
the two-dimensional photoelectric detector is a CCD, a CMOS, a two-dimensional photocell array or a two-dimensional photodiode array.
A method of wavefront sensing using said wavefront sensor, the sensing method comprising the steps of:
1) the wave front to be measured is incident on the mixed grating, and the generated interference pattern is recorded on the two-dimensional photoelectric detector; for known wavefront sensor geometry and numerical aperture of the incident light wave, the system shear rate β can be uniquely determined;
2) fourier transform is carried out on interference patterns collected by a two-dimensional photoelectric detector to obtain corresponding spectrogram, secondary spectrums in the x direction and the y direction are selected by a filtering method, the selected secondary spectrums are respectively translated to the center and subjected to inverse Fourier transform, and differential wave fronts delta W in the x direction and the y direction are respectively obtained after phase unwrappingxAnd Δ Wy；
3) From the differential wavefront information Δ W using a wavefront reconstruction algorithmxAnd Δ WyThe measured wavefront W (x, y) is obtained by reduction.
Compared with the prior art, the invention has the beneficial effects that:
when the grating is used for four-wave front shearing interference, the grating has better diffraction spectrum characteristics than the improved Hartmann mask widely used at present, namely higher +/-1-order diffraction efficiency, so that the system error in the differential wave front extraction process is further reduced, and the measurement precision is improved; by properly selecting the quantization factor N of the amplitude grating, the grating structure can be simplified on the premise of ensuring the diffraction efficiency, and the processing difficulty of components is reduced.
Drawings
FIG. 1 is a block diagram of a wavefront sensor based on a modified Hartmann mask;
FIG. 2 is a top view of an amplitude grating with a light transmitting area that is approximately circular;
FIG. 3 is a schematic diagram of a rectangular mosaic of the amplitude grating near-transmission regions;
fig. 4 is a schematic diagram of the stitching effect corresponding to different quantization factors N, where (a) - (j) are respectively N ═ 1,2,. 10;
FIG. 5 is a top view of the actual etched area of the checkerboard phase grating;
FIG. 6 is a top view of a hybrid grating structure;
FIG. 7 is a side view of a hybrid grating profile;
FIG. 8 is a flow chart of a method of using the wavefront sensor for wavefront measurement;
fig. 9 is a schematic of the geometry of the wavefront sensor.
Detailed Description
In order to make the contents, implementation processes and advantages of the present invention clearer, the following description of the present invention is made with reference to the following examples and accompanying drawings, but the scope of the present invention is not limited by the examples. The following numbers in parentheses correspond to the numbers in the drawings of the specification.
A wave front sensor based on improved Hartmann mask comprises a diffraction optical element 1-2 and a two-dimensional photoelectric detector 1-4, wherein the diffraction optical element is a two-dimensional grating structure with the same period in the orthogonal direction and is formed by mixing an amplitude grating 1-2-1 with the period of T and a light transmission area of approximate circle and a chessboard-shaped phase grating 1-2-2 with the period of 2T and the phase gradient of pi under the central wavelength; the diffraction optical element and the two-dimensional photoelectric detector are in a position relation that the diffraction optical element and the two-dimensional photoelectric detector are sequentially arranged along the transmission direction of the measured wavefront and are connected through a connecting mechanism 1-3.
Aiming at a shearing interference wave aberration detection system with the central working wavelength of 532nm, the invention can be made into the following forms:
the pitch of the diffractive optical element 1-2 was 55 μm, the grating size was 15mm × 15mm, and the substrate thickness Z was2Is 3 mm.
The light-transmitting area is an approximately circular amplitude grating 1-2-1, and the amplitude transmittance of the light-transmitting area under a plane rectangular coordinate system has the following form:
wherein, T is the period of the amplitude grating, circ () is the circular domain function, a is the radius of the circular light-transmitting area of the amplitude grating, and (b) is the dirac delta function.
In this example, the period T of the amplitude grating is 27.5 μm, and the thickness of the light-shielding metal layer is > 200 nm. The value of the radius a of the light-transmitting area is expressed by an equation
The first non-zero root of (1), wherein J1Is a first order class Bessel function. The numerical analysis result was 10.6157 μm.
The light transmission area in each quadrant of the amplitude grating is a non-rectangular figure which is formed by splicing a plurality of rectangles and is approximate to 1/4 circle. The number of rectangles used for splicing in each quadrant is N, N is a quantization factor, and N is more than or equal to 2. (FIG. 3, FIG. 4). In this example, each 1/4 circular field is formed by 4 rectangles spliced together, i.e., the quantization factor N is 4 (fig. 4 (d)). The geometric parameters of the rectangle are a series of angles theta formed by the intersection point of the rectangular frame and the circumference and the coordinate axis1,θ2,...θ8Is uniquely determined and satisfied
Where j is 1, 2.. 8, the seed value θ is iterated1＝13.34°。
The checkerboard phase grating (figure 7) is manufactured by adopting an etching method, and the phase delay of the phase grating is enabled to be proper by selecting the proper etching depth h
For a given system parameter, the magnitude of h is determined by the center wavelength λ of the incident light wave and the refractive index n of the phase grating medium. The etching depth of the phase grating described in this example satisfies the relationship:
the diffraction grating element is formed by mixing an amplitude grating and a phase grating, and in the actual processing process, the etching can only meet the following requirements:
and the areas not covered by the amplitude grating mask (circular gray areas in fig. 5) are sufficient.
In this example, the phase grating 1-2-2 has a period 2T of 55 μm, the substrate medium is quartz of corning 7980F, the refractive index n is 1.46, and the etching depth corresponds to
Two-dimensional photodetectors use CCD sensors with a resolution of 640 x 480, a single pixel size of 9.9 μm (h) x 9.9 μm (v).
The length of the connecting mechanism 1-3 is adjusted to ensure that the distance Z between the grating emergent plane and the CCD photosensitive surface3(FIG. 9) is 0.7 mm.
With a system NA of 0.3, a variable shear rate of 1.2526% -2.1435% can be achieved. The number of interference fringes is 30-102, and the width of single fringe is more than 4 pixels.
When the wavefront sensor is used for four-wave transverse shear interference, the proportion of the intensities of four orders (+1, +1), (+1, -1), (-1, +1) and (-1, -1) mainly participating in interference to the sum of the intensities of all diffraction orders is used as an index for evaluating the diffraction efficiency of the wavefront sensor. The diffraction efficiency of the wavefront sensor in this example is 81.66%, and the diffraction efficiency of the wavefront sensor using MHM as the diffraction element under the same condition is 80.04%, so that the systematic error caused by interference between higher diffraction orders can be effectively reduced in practical use.
A method for performing wavefront detection by using the wavefront sensor comprises the following steps:
1) the wavefront 1-1 to be measured is incident on the mixed grating 1-2, and the generated interference pattern 8-3 is recorded on the two-dimensional photoelectric detector 1-4; for known wavefront sensor parameters (shown in FIG. 9, distance Z of equivalent point source facet 9-1 from grating entrance facet 9-2-11Thickness Z of the grating substrate2The distance Z between the emergent surface of the grating and the photosensitive surface 9-3 of the detector3) And the numerical aperture of the incident light wave, the system shear rateβ can be uniquely identified;
2) fourier transform is carried out on an interferogram 8-3 collected by a two-dimensional photoelectric detector to obtain a corresponding spectrogram 8-4, secondary spectrums in the x direction and the y direction are selected by a filtering method, the selected secondary spectrums are respectively translated to the center and subjected to inverse Fourier transform, and phase unwrapping is carried out to respectively obtain differential wavefronts delta W in the x direction and the y directionxAnd Δ Wy；
3) From the differential wavefront information Δ W using a wavefront reconstruction algorithmxAnd Δ WyThe measured wavefront W (x, y)8-5 is obtained by reduction.
Claims (4)
1. A wave front sensor based on Hartmann mask is characterized by comprising a diffraction optical element and a two-dimensional photoelectric detector which are sequentially arranged along the transmission direction of the wave front to be detected, wherein the diffraction optical element is a two-dimensional grating structure with the same period in the orthogonal direction and is formed by mixing an amplitude grating with the period of T and a circular light-transmitting area and a chessboard-shaped phase grating with the period of 2T and the phase gradient of pi under the central wavelength; establishing a plane rectangular coordinate system by taking the circle center of the amplitude grating with the light-transmitting area as a circle as the origin of coordinates, and uniformly dividing the circle into four quadrants, wherein 1/4 circles in each quadrant are formed by splicing N rectangles, and N is more than or equal to 2; the amplitude transmittance of a circular amplitude grating in a planar rectangular coordinate system has the following form:
wherein, the circ () is a circular domain function, the (-) is a Dirac delta function, and the radius of the circular amplitude grating light-transmitting area a is an equation
The first non-zero root of (1), wherein J1Is a first-order Bessel function; the amplitude transmittance of the checkerboard phase grating meets the following form:
where rect () is a rectangular function, j is 1,2 … N,
2. the hartmann mask-based wavefront sensor of claim 1, wherein the diffractive optical element and the two-dimensional photodetector are coupled by a coupling mechanism.
3. The Hartmann mask-based wavefront sensor of claim 1 or 2, wherein the two-dimensional photodetector is a CCD, a CMOS, a two-dimensional photocell array, or a two-dimensional photodiode array.
4. A method of wavefront sensing using the wavefront sensor of claim 1, the method comprising the steps of:
firstly, an interference pattern generated when a wavefront to be measured is incident on a diffraction optical element is recorded on a two-dimensional photoelectric detector;
② Fourier transform interference pattern collected by the two-dimensional photodetector to obtain corresponding spectrogram, filtering to select secondary spectrums in x and y directions, translating the selected secondary spectrums to the center of spectrogram respectively, performing inverse Fourier transform, phase unwrapping to obtain differential wavefront Δ W in x and y directions respectivelyxAnd Δ Wy；
③ use wavefront reconstruction algorithm to derive differential wavefront information Δ W from the wavefrontxAnd Δ WyThe measured wavefront is obtained by reduction.
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| CN110441992B (en) | 2019-07-23 | 2020-05-05 | 中国科学院上海光学精密机械研究所 | Projection objective wave aberration detection device and detection method |
| CN110736544B (en) * | 2019-10-08 | 2021-11-30 | 中国科学院上海光学精密机械研究所 | Shear amount calibration device and calibration method for transverse shear interference wavefront sensor |
| CN111595559B (en) * | 2020-06-22 | 2021-05-25 | 中国科学院长春光学精密机械与物理研究所 | First-order wavefront error measuring system of non-continuous mirror telescope |
| CN112034688B (en) * | 2020-08-11 | 2021-07-27 | 中国科学院上海光学精密机械研究所 | Projection objective wave aberration detection device and detection method for improving detection speed |
| EP3964809A1 (en) * | 2020-09-02 | 2022-03-09 | Stichting VU | Wavefront metrology sensor and mask therefor, method for optimizing a mask and associated apparatuses |
| CN112730354B (en) * | 2020-12-14 | 2022-11-01 | 南方科技大学 | Structured light imaging method, imaging graph and application in biochemical detection |
| CN112945513A (en) * | 2021-03-16 | 2021-06-11 | 张家港奥珩光电科技有限公司 | Wind tunnel test section air density measurement system based on four-wave shearing interferometer |
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| CN106647176A (en) * | 2015-10-30 | 2017-05-10 | 上海微电子装备有限公司 | Wave aberration measurement device and method |
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| DE19538747A1 (en) * | 1995-10-18 | 1997-04-24 | Johannes Prof Dr Schwider | Planar wavefront aberration measuring method for coherent light source in gitter shear interferometer |
| CN106647176A (en) * | 2015-10-30 | 2017-05-10 | 上海微电子装备有限公司 | Wave aberration measurement device and method |
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| Title |
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| Je＇roˆme Primot and Nicolas Gue＇rineau.Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard.《APPLIED OPTICS》.2000,第5715页右栏第3段-第5720页右栏第2段以及图1-9. * |
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