CN108955905A - Wavefront sensor and detection method based on modified Hartmann's mask - Google Patents

Abstract

The invention relates to a wavefront sensor and a detection method based on an improved Hartmann mask with a circular light-transmitting region. The wavefront sensor includes a diffraction element and a detector, wherein the diffraction element is a hybrid grating composed of a checkerboard-shaped phase grating and an amplitude grating with a circular light-transmitting area. When used for four-wavefront shear interference, it has a relatively The widely used Modified Hartmann Mask (MHM) has better diffraction spectrum characteristics, that is, higher ±1-order diffraction efficiency, thereby further reducing the systematic error in the differential wavefront extraction process and improving the measurement Accuracy; by properly selecting the quantization factor of the amplitude grating, the grating structure can be simplified under the premise of ensuring the diffraction efficiency, and the processing difficulty of components can be reduced. The device can be used in the field of high-precision wavefront detection.

Description

Wavefront sensor and detection method based on improved Hartmann mask

technical field

The invention belongs to the field of optical wavefront detection, in particular to a shear interference wavefront sensor and detection method based on amplitude and phase hybrid gratings.

Background technique

High-precision wavefront measurement technology is widely used in the fields of surface shape detection of optical components, wave aberration measurement of high-resolution optical systems, astronomical observation, high-energy laser beam quality evaluation, and in vivo imaging of biological tissues.

Shearing interferometry is a typical wavefront interferometry technique that does not require a standard mirror. The wavefront to be measured interferes with the superposition of the sheared wavefront after its own misalignment. Compared with traditional interference techniques such as phase-shift point diffraction interference, shearing interference technology can simplify the optical path structure and reduce the difficulty of operation because it does not rely on standard mirrors or pinhole diffraction to generate the required reference wavefront. It has a large dynamic range, With the advantages of easy integration and instrumentation, it is often used to test the surface shape of large optical components. In addition, shear interference is less affected by air turbulence and mechanical vibrations than traditional interferometry techniques because the two interfering beams are nearly equi-optical.

Grating shearing interference technology uses gratings as spectroscopic elements, which has the advantages of simple device structure, low processing difficulty, and easy system integration. At the same time, it avoids the systematic errors introduced by the use of prisms, beam splitters, mirrors and other structures, and improves the overall measurement accuracy. Grating beam-splitting structures are widely used in transverse shearing interferometry, such as the classic Ronchi test. In 1997, Schreiber et al. proposed a lateral shearing interference device based on two Ronchi phase grating structures, which realized the lateral shearing interference between ±1st-order diffracted light (Schreiber, H., and J.Schwider."Lateral shearing interferometer based on two Ronchi phase gratings inseries."Applied optics 36.22(1997):5321-5324.).

However, the traditional transverse shearing interferometry generally requires two measurements in the orthogonal direction, and then synthesizes the final wavefront to be obtained. This asynchronous exposure process increases the complexity of the measurement process and introduces systematic errors, which limits the The precision and usage scenarios of the technology. Therefore, researchers began to focus on multi-surface transverse shearing interferometry.

In 1993, Primot proposed a three-wave lateral shearing interference device using a prism for splitting and shearing (Primot, Jerome. "Three-wave lateral shearing interferometer." Applied optics 32.31 (1993): 6242-6249.). The three replicated beams are sheared and superimposed at an angle of 120° to each other, and phase gradients in three directions are generated in the same interferogram, and then the wavefront gradient values in two directions are obtained by projection method, and the final solution is to be solved Find the wave front. However, this method requires high processing precision of the spectroscopic element, which limits its measurement precision. In 1995, Primot and Sogno redesigned the wavefront beam splitting scheme on the basis of the previous three-wave transverse shearing interference device, using a bidirectional hexagonal etched structure grating to achieve wavefront beam splitting. This improvement realizes the accuracy of the wave loss direction of the split wavefront, and makes it possible for the grating structure to be used as a multi-wavefront splitting element.

In 2000, Primot and Guérineau proposed an improved Hartmann mask (Modified Hartmann Mask, MHM) on the basis of the traditional Hartmann method. By adding a phase grating, the diffraction characteristics of the Hartmann mask were improved to concentrate the energy Distributed on the four diffraction orders involved in interference (Primot J, Guérineau N. Extended Hartmann test based on the pseudoguiding property of a Hartmannmask completed by a phase chessboard[J]. Applied optics, 2000, 39(31): 5715-5720 .). The MHM grating structure is composed of a checkerboard phase grating and a rectangular amplitude grating, the duty ratio of the amplitude grating is 2/3, and the phase grating period is 2 times of the amplitude grating period. In the case of the central wavelength, all even-numbered and ±3-order diffracted lights in the diffraction field of the MHM grating structure are eliminated, and only ±1-order diffracted lights exist in ±4 orders, so the order selection window is not required to obtain Measure the phase information of the wavefront. In 2004, Velghe, Primot and Guérineau used the improved Hartmann mask for multi-beam shearing interference technology, and proposed the concept of four-wave transverse shearing interference (Velghe, Sabrina, et al. "Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers." Optics letters 30.3 (2005): 245-247.). Experiments show that compared with the traditional two-beam shearing interference, the four-beam shearing interference technology can obtain a higher signal-to-noise ratio, thereby improving the measurement accuracy. Four-wave transverse shear interferometry has the advantages of compact device, achromatic, large dynamic range and high accuracy. However, the MHM grating structure still retains high-order diffraction orders such as ±5 and ±7, which will affect the interference between ±1-order diffracted light in the x and y directions during the actual measurement process, which limits the further improvement of measurement accuracy .

In 2015, Ling et al. proposed a randomly encoded hybrid grating structure based on luminous flux constraints (Ling T, Liu D, Yue X, et al. Quadriwave lateral shearing interferometer based on randomly encoded hybrid grating[J]. Optics letters, 2015 , 40(10):2245-2248.). Based on the MHM grating structure, this structure constrains the luminous flux of the amplitude grating by means of random coding, so that the transmittance function of the amplitude grating approximately satisfies the ideal cosine half-wave form, and eliminates all the parameters except ±1 order in principle. Diffraction orders form an approximately ideal four-wave interference model, which further improves the detection accuracy of the wavefront to be measured. However, the design of random coding poses challenges to the processing of amplitude gratings, and the processing yield is relatively low, which limits the application scenarios of random coding hybrid gratings.

Contents of the invention

The object of the present invention is to provide a wavefront sensor and detection method based on an improved Hartmann mask by combining the advantages of the above-mentioned prior art and overcoming the shortcomings of the above-mentioned prior art. A hybrid grating composed of a nearly circular amplitude grating in the light-transmitting area and a checkerboard phase grating is used as the diffraction light-splitting element. On the one hand, compared with the modified Hartmann mask (MHM) widely used at present, the intensity of high-order diffraction orders is further suppressed, and the systematic error in the process of differential wavefront extraction is reduced in principle; on the other hand, , compared with the random coded hybrid grating (REHG) whose diffraction characteristics are close to the ideal situation, under the premise of ensuring the ±1st order diffraction efficiency, it reduces the difficulty of processing and manufacturing, so it has a wider range of applications.

Technical solution of the present invention is as follows:

A wavefront sensor based on an improved Hartmann mask, including a diffractive optical element and a two-dimensional photodetector, the diffractive optical element is a two-dimensional grating structure with the same period in the orthogonal direction, and the period is T , the light-transmitting region is composed of an approximately circular amplitude grating and a checkerboard phase grating with a period of 2T and a phase gradient of π at the central wavelength; the positional relationship between the diffractive optical element and the two-dimensional photodetector is: The transmission direction of the wavefront to be measured is a diffractive optical element and a two-dimensional photodetector in turn.

The light-transmitting region is an approximately circular amplitude grating, and its amplitude transmittance has the following form in the plane Cartesian coordinate system:

Among them, T is the period size 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 δ() is the Dirac delta function.

The light-transmitting area is an approximately circular amplitude grating, and the shape of the light-transmitting area in each quadrant is an approximately 1/4 circular non-rectangular figure spliced by N rectangles, where N is a quantization factor, And N≥2. The geometric parameters of the rectangle are uniquely determined by a series of angles θ ₁ , θ ₂ ,...θ _2N formed by the intersection points of the rectangle frame and the circumference and the coordinate axes, and satisfy The recurrence relationship of , where j=1,2,...2N, the initial value of iteration

The light-transmitting region is an approximately circular amplitude grating, and the radius a of the light-transmitting region takes the equation numerically The first nonzero root of , where J ₁ is the first-order Bessel function of the first kind.

The amplitude transmittance of the checkerboard phase grating satisfies the following form:

Among them, T is the period size of the amplitude grating, is the phase retardation of the phase grating under the irradiation of the central wavelength,

The two-dimensional photodetector is CCD, CMOS, two-dimensional photocell array, two-dimensional photodiode array, two-dimensional photodetector array with pinhole or slit diaphragm, two-dimensional photodetector with fluorescence conversion sheet arrays, two-dimensional photodetector arrays with fiber optic faceplates.

A method for wavefront detection using the wavefront sensor, the detection method comprising the following steps:

1) The wavefront to be measured is incident on the hybrid grating, and the resulting interferogram is recorded on the two-dimensional photodetector; for the known geometric parameters of the wavefront sensor and the numerical aperture of the incident light wave, the system shear rate β can be calculated by uniquely determined;

2) Perform Fourier transform on the interference pattern collected by the two-dimensional photodetector to obtain the corresponding spectrum diagram, select the secondary spectrum in the x and y directions by filtering method, and shift the selected secondary spectrum to the center respectively And inverse Fourier transform is performed, and the differential wavefronts ΔW _x and ΔW _y in the x and y directions are respectively obtained after the phase is unwrapped;

3) Using the wavefront reconstruction algorithm to restore the measured wavefront W(x, y) from the differential wavefront information ΔW _x and ΔW _y .

Compared with prior art, the beneficial effect of the present invention:

Using a hybrid grating composed of a checkerboard phase grating and an approximately circular amplitude grating in the light-transmitting area as a diffraction element, it has an improved Hartmann mask that is more widely used than the currently widely used Hartmann mask when used for four-wavefront shear interference Better diffraction spectrum characteristics, that is, higher ±1-order diffraction efficiency, which further reduces the systematic error in the process of differential wavefront extraction and improves measurement accuracy; by properly selecting the quantization factor N of the amplitude grating, it can ensure that the diffraction Simplify the grating structure under the premise of efficiency, and reduce the processing difficulty of components.

Description of drawings

Fig. 1 is a structural diagram of a wavefront sensor based on an improved Hartmann mask;

Fig. 2 is a top view of an amplitude grating whose light-transmitting region is approximately circular;

Fig. 3 is a schematic diagram of rectangular splicing of the near light-transmitting area of the amplitude grating;

Fig. 4 is a schematic diagram of splicing effects corresponding to different quantization factors N, wherein (a)-(j) are effect diagrams when N=1, 2, ... 10;

Fig. 5 is a top view of the actual etching area of the checkerboard phase grating;

Figure 6 is a top view of the hybrid grating structure;

Figure 7 is a side view of a cross section of a hybrid grating;

Fig. 8 is the flow chart of the method that described wavefront sensor is used for wavefront measurement;

Fig. 9 is a schematic diagram of the geometric structure of the wavefront sensor.

Detailed ways

In order to make the content, implementation process and advantages of the present invention clearer, the present invention will be further described below in conjunction with embodiment and accompanying drawing, but do not limit protection scope of the present invention with this embodiment. The numbers in the following brackets correspond to the numbers in the accompanying drawings of the specification.

A wavefront sensor based on an improved Hartmann mask, including a diffractive optical element 1-2 and a two-dimensional photodetector 1-4, the diffractive optical element is a two-dimensional grating with the same period in the orthogonal direction The structure is composed of an amplitude grating 1-2-1 with a period of T and an approximately circular light-transmitting region and a checkerboard phase grating 1-2-2 with a period of 2T and a phase gradient of π at the central wavelength; The positional relationship between the diffractive optical element and the two-dimensional photodetector is that, along the transmission direction of the measured wavefront, there are the diffractive optical element and the two-dimensional photodetector in sequence, and the two are connected by the connecting mechanism 1-3.

For the shearing interference wave aberration detection system whose central operating wavelength is 532nm, the present invention can be made into the following form:

The grating pitch of the diffractive optical element 1-2 is 55 μm, the grating size is 15 mm×15 mm, and the substrate thickness Z ₂ is 3 mm.

The light-transmitting area is an approximately circular amplitude grating 1-2-1, and its amplitude transmittance has the following form in the plane Cartesian coordinate system:

Among them, T is the period size 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 δ() 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 obtained by the equation The first nonzero root of , where J ₁ is the first-order Bessel function of the first kind. The numerical analysis result is 10.6157 μm.

The light-transmitting area is an approximately circular amplitude grating, and the shape of the light-transmitting area in each quadrant is an approximately 1/4 circular non-rectangular figure spliced by N rectangles, and N is a quantization factor ( Figure 3, Figure 4). In this example, each 1/4 circular domain is formed by splicing 4 rectangles, that is, the quantization factor N=4 ( FIG. 4( d )). The geometric parameters of a rectangle are uniquely determined by a series of angles θ ₁ , θ ₂ ,...θ ₈ formed by the intersection points of the rectangle border and the circumference and the coordinate axes, and satisfy The recurrence relation of , where j=1,2,...8, iteration seed value θ ₁ =13.34°.

The checkerboard phase grating (Figure 7) is fabricated by etching, and the phase delay of the phase grating can be made by selecting the appropriate etching depth h For a given system parameter, the size of h is jointly determined by the central 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 composed of a mixture of amplitude grating and phase grating. In the actual processing process, it only needs to be etched to meet:

And the area not covered by the amplitude grating mask is sufficient (the circular gray area in FIG. 5 ).

In this example, the phase grating 1-2-2 period 2T=55μm, the substrate medium is Corning 7980F quartz, the refractive index n=1.46, and the corresponding etching depth

The two-dimensional photodetector uses a CCD sensor with a resolution of 640*480 and a single pixel size of 9.9μm(H)×9.9μm(V).

Adjust the length of the connection mechanism 1-3 so that the distance Z ₃ (Fig. 9) between the grating exit plane and the photosensitive surface of the CCD is 0.7mm.

In the case of system NA=0.3, a variable shear rate of 1.2526%-2.1435% can be achieved. The number of interference fringes is between 30-102, and the width of a single fringe is >4 pixels.

When the wavefront sensor is used for four-wave transverse shear interference, four major orders (+1, +1), (+1,-1), (-1,+1) and ( The ratio of the intensity of -1, -1) to the sum of all diffraction order intensities is used as an index to evaluate the diffraction efficiency of the wavefront sensor. The diffraction efficiency of the wavefront sensor described in this example is 81.66%, while the diffraction efficiency of the wavefront sensor using MHM as the diffraction element is 80.04% under the same conditions, so it can effectively reduce the gap between high-order diffraction orders in actual use. System errors caused by interference.

A method for wavefront detection using the wavefront sensor, comprising the steps of:

1) The wavefront 1-1 to be measured is incident on the hybrid grating 1-2, and the resulting interferogram 8-3 is recorded on the two-dimensional photodetector 1-4; for known wavefront sensor parameters (as shown in 9, the distance Z ₁ between the equivalent point light source surface 9-1 and the incident surface 9-2-1 of the grating, the thickness Z ₂ of the grating substrate, the distance Z ₃ between the exit surface of the grating and the photosensitive surface 9-3 of the detector) and the incident The numerical aperture of the light wave, the system shear rate β can be uniquely determined;

2) Perform Fourier transform on the interferogram 8-3 collected by the two-dimensional photodetector to obtain the corresponding spectrogram 8-4, select the secondary spectrum in the x and y directions by filtering, and convert the selected two The first-order spectrum is translated to the center and inverse Fourier transform is performed, and the differential wavefronts ΔW _x and ΔW _y in the x and y directions are respectively obtained after unpacking the phase;

3) Using the wavefront reconstruction algorithm to restore the measured wavefront W(x, y) 8-5 from the differential wavefront information ΔW _x and ΔW _y .

Claims (6)

1. A wavefront sensor based on an improved Hartmann mask, characterized in that it comprises a diffractive optical element and a two-dimensional photodetector placed successively along the measured wavefront transmission direction, it is characterized in that the diffraction The optical element is a two-dimensional grating structure with the same period in the orthogonal direction. It is composed of an amplitude grating with a period of T and a nearly circular light-transmitting area and a checkerboard phase grating with a period of 2T and a phase gradient of π at the central wavelength. composition. 2 . The wavefront sensor based on the improved Hartmann mask according to claim 1 , wherein the diffractive optical element and the two-dimensional photodetector are connected by a connecting mechanism. 3 . 3. The wavefront sensor based on the improved Hartmann mask according to claim 1 or 2, wherein the shape of the light-transmitting region of the amplitude grating in each quadrant is spliced by N rectangles The approximate 1/4 circular non-rectangular figure formed, and N≥2. 4. The wavefront sensor based on the improved Hartmann mask according to claim 1 or 2 is characterized in that the radius a of the light-transmitting region of the amplitude grating is an equation The first non-zero root of , where J ₁ is the first-order Bessel function of the first kind, and T is the period of the amplitude grating. 5. the wavefront sensor based on improved Hartmann mask according to claim 1 or 2, is characterized in that, described two-dimensional photodetector is CCD, CMOS, two-dimensional photocell array, two-dimensional photodiode arrays, two-dimensional photodetector arrays with pinhole or slit apertures, two-dimensional photodetector arrays with fluorescence conversion plates, or two-dimensional photodetector arrays with fiber optic panels. 6. A method adopting the wavefront sensor according to claim 1 to carry out wavefront detection, is characterized in that the method comprises the steps: ① The interference pattern generated by the wavefront to be measured incident on the diffractive optical element is recorded on the two-dimensional photodetector; ② Perform Fourier transform on the interference pattern collected by the two-dimensional photodetector to obtain the corresponding spectrogram, select the secondary spectrum in the x and y directions by filtering method, and translate the selected secondary spectrum to the spectrogram respectively Center and carry out inverse Fourier transform, and get the differential wavefronts ΔW _x and ΔW _y in the x and y directions respectively after unwrapping the phase; ③The wavefront reconstruction algorithm is used to restore the measured wavefront W(x,y) from the differential wavefront information ΔW _x and ΔW _y .