WO2022158957A1 - Coded diffraction pattern wavefront sensing device and method - Google Patents

Abstract

Optical system for controlling optical aberrations incorporating coded diffraction patterns, comprising: a wavefront phase corrector device; beam splitter; image sensor; a wavefront sensor module, comprising signal processor; phase correction driver, connected with the processor and the wavefront phase corrector; the phase corrector receives a light beam and controllably optically transfers light beam to beam splitter; beam splitter splits light beam received into two optical beams: original wavefront part and wavefront sensing part, optically sends original wavefront part of light beam to image sensor and wavefront sensing part of the light beam - to the wavefront sensor module which comprises a processor, a collimation telescope; one or more beam splitters adapted to split the light beam received from the telescope into two optical beams; one or more amplitude masks, adapted to produce diffraction patterns; an optical system; and image sensor, adapted to convert the light intensity signal to digital.

Description

Coded diffraction pattern wavefront sensing device and method

Field of the Invention

The invention relates to the field of optics, optical systems; wavefront sensing and correction solutions applicable to various signal transmission applications, improvement of the quality of optical systems in astronomy, microscopy, retinal imaging, metrology, communication.

Background of the Invention

The resolution of optical systems is limited to wavefront distortions caused by dynamic turbid media, like biological tissues or atmosphere. Optical aberrations caused by turbulence can be corrected using adaptive optics techniques, but before those must be measured. In astronomy, optical communications, metrology and microscopy, optical wavefront distortions are measured using wavefront sensors (WFS).

A wavefront sensor is a device for measuring the aberrations of an optical wavefront. Typical wavefront sensors comprise (i) an optical device, which is adapted to transform the wavefront aberration (shift of ideal planar wave) into intensity variations or local spatial displacements; (ii) a detector, such as a CCD, or CMOS, adapted to transform light into voltage and (hi) a reconstructor of the light- to -voltage digital signal into meaningful wavefront, applicable to wavefront corrector.

The most popular wavefront sensing technique is Shack-Hartmann (SH) type sensor [1], according to which a lenslet matrix is used to find the shifts or light rays from the ideal ray pattern on the detector. A reference laser star is often required to perform wavefront correction tasks in astronomy with the Shack-Hartmann sensor type. Natural stars are too weak to be used to measure optical error with Shack-Hartmann wavefront sensors. This method also has number of physical limitations: Shack- Hartmann sensors require large image sensors, are not optimal performance with extended sources, poor sensitivity at low modes, as also wavefront warping can happen. Other most popular are the Phase diversity and Curvature sensors; which are using phase retrieval algorithms. These WF sensors provide benefits over SH sensor in the number of detector pixels required to measure the wavefront, and therefore a large saving in both cost and overall size. Method is well suited for tilt measurements and low order aberrations. As also phase diversity sensors can be applied directly to corrective optics.

The method recently proposed by Wang et al [2,3] uses binary mask to detect the wavefront aberrations. It adapts the idea of Shack-Hartman sensor while replace the lenslet matrix with a binary coded structure. In the Coded Wavefront Sensor introduced by Wang et al, the slope of the wavefront is tracked using numerical methods related to optical flow. To find the phase a pixel shifts or apparent motion [a] is registered for sensor pixel size d_s in the following equation,

where z is a distance from binary mask to sensor, A - wavelength. Numerical solver of the Wang et al. method is inspired by optic flow mathematics.

Quadriwave lateral shearing interferometry, utilizes modified Hartmann mask technique. Diffractive grating replicates the incident beam into four identical waves, as a result which create an interference pattern on the image detector. The interference fringe deformations encode the phase gradients. It allows to measure the phase and intensity of a beam with a high spatial resolution.

Nevertheless, due to specifics of each method there is a need for advanced methods, especially for WFS of higher sensitivity and robust to noise for application inastronomy, microscopy and free space optical communication.

Summary of the Invention

The goal of the invention is to eliminate the drawback of the prior art solutions. The set goal is reached by providing a wavefront sensor incorporating means for phase retrieval, using numerical algorithms that operate in low signal and noise conditions. The method proposed is applicable for the detection of weak objects because the incoming beam is not divided into many sub-beams. The proposed device acquires an image of the wavefront intensity, which is encoded by number of binary amplitude, or phase masks, or apertures and uses a mathematical phase retrieval algorithm to recover the wavefront from the set of intensity images.

In the proposed embodiment optical system for controlling optical aberrations incorporating coded diffraction patterns, comprising: a wavefront phase corrector device; a beam splitter; an image or signal sensor; a wavefront sensor module, comprising a signal processor; a phase correction driver, electrically connected with the processor and the wavefront phase corrector; the phase corrector is designed to be able to receive a light beam from a light beam source and controllab ly optically transfer the light beam to the beam splitter; the beam splitter is designed to split the light beam received into two optical beams: the original wavefront part and the wavefront sensing part, as well as optically send the original wavefront part of the light beam to the image or signal sensor and the wavefront sensing part of the light beam - to the wavefront sensor module; the wavefront sensor module comprising the processor, a collimation telescope; one or more beam splitters, optically connected to the collimation telescope and adapted to split the light beam received from the telescope into two optical beams; one or more amplitude masks, adapted to produce diffraction patterns; an optical system; and image sensor, adapted to convert the light intensity signal to digital; the beam splitters are further adapted to optically send the light beam through the amplitude masks, or phase masks, or apertures to the optical system, where the optical system is adapted to optically focus diffraction patterns produced by mentioned elements, which are optically received from the beam splitters, on the image sensor; wherein the processor comprises instructions for

(a) digitizing images formed at the image sensor,

(b) extracting intensity images of diffraction patterns or individual PSFs from the digitized images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations;

(c) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values;

(d) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase information; (e) removing noises and phase retrieval artefacts from the obtained information;

(f) extrapolating retrieved phase data from the phase information obtained at previous step.

The proposed process for controlling optical aberrations incorporating coded patterns, comprising the following steps:

(i) providing a light beam to a phase corrector;

(ii) directing light from the phase corrector to a beam splitter;

(hi) splitting the light beam by the beam splitter into two optical beams: the original wavefront part and the wavefront sensing part;

(iv) directing the original light beam to an image or signal sensor, directing the wavefront sensing beam to the wavefront sensor module to convert the light signal to digital signal;

(v) processing the digital signal obtained in the image processor to retrieve phase data;

(vi) sending phase data for input to the phase correction processor and driver;

(vii) providing the phase correction driver with phase conjugate data to the phase corrector;

(viii) correcting an optical phase by the phase corrector, thereby changing the wavefront of the incoming light beam; wherein processing the signal obtained in the processor to form phase data at the step

(v) comprises the following steps:

(g) digitizing images formed at the image sensor,

(h) extracting intensity images of diffraction patterns or individual PSFs from the digitized images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations;

(i) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values;

(j) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase matrix data;

(k) removing noises and retrieval artefacts from the obtained phase matrix data; (1) extrapolating phase data and phase surface from the phase matrix data obtained at previous step.

Brief Description of Drawings

Fig. 1 - schematic representation of the optical circuit of the wavefront sensor with wavefront beam splitter block and amplitude or phase masks according to the invention;

Fig. 2 - illustrates the total digital signal processing workflow within a mathematical algorithm with analytical elements;

Fig. - 3 shows the flowchart of the scheme of processing signals received from the image sensor;

Fig. - 4 shows the diffraction scenes of the image processing flow and wavefront correction path.

Fig. - 5 shows two pseudorandom masks in circular optical window arranged in a row, with a potential position of light beams.

Detailed Description of the Invention

The optical system for controlling optical aberrations incorporating coded patterns, comprising: a wavefront phase corrector device 20; a beam splitter 11; an image or signal sensor 15; a wavefront sensor module 30, comprising a signal processor 40; a phase correction driver 21, electrically connected with the signal processor 40 and the wavefront phase corrector 20; the phase corrector 20 is designed to be able to receive a light beam from a light beam source and controllably optically transfer the light beam to the beam splitter 11; the beam splitter 11 is designed to splitthe light beam received into two optical beams: the original wavefront part 2 and the wavefront sensing part 3, as well as optically send the original wavefront part 2 of the light beam to the image or signal sensor 15 and the wavefront sensing part 3 of the light beam - to the wavefront sensor module 30; the wavefront sensor module 30 comprising the signal processor 40, a collimation telescope 31; one or more beam splitters 32, 33, ..., optically connected to the collimation telescope 31 and adapted to splitthe light beam received from the telescope 31 into two optical beams; one or more amplitude masks 36 (e.g. as shown on Fig. 5), adapted to produce diffraction patterns; an optical system 34; and image sensor 37, adapted to convert the light intensity signal to digital; the beam splitters 32, 33, ... are further adapted to optically send the light beam 5, 6 through the amplitude masks 36 to the optical system 34, where the optical system 34 is adapted to optically focus diffraction patterns produced by the masks 36, which are optically received from the beam splitters 32, 33, ..., on the image sensor 37; wherein the processor 40 comprises instructions for: (a) digitizing images formed at the image sensor 37, (b) extracting intensity images of diffraction patterns or individual PSFs from the digitized images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations; (c) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values; (d) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase matrix data; (e) removing noises and retrieval artefacts from the obtained phase matrix data; (f) extrapolating phase data and phase surface from the phase matrix data obtained at previous step.

The amplitude masks 36 and the divided beams 5, 6, ... can be spatially arranged in a row, or a matrix. The image sensor 37 can be a CMOS image sensor, CCD or other known sensitive array. The phase corrector 20 can comprise a deformable mirror or a spatial light modulator.

The process for controlling optical aberrations incorporating coded diffraction patterns, comprises the following steps: (i) providing a light beam to a phase corrector 20; (ii) directing light from the phase corrector 20 to a beam splitter 11; (hi) splitting the light beam in the beam splitter 11 into two optical beams: the original wavefront part 2 and the wavefront sensing part 3; (iv) directing the reference wavefront light beam part 2 to an image or signal sensor 15, directing the wavefront sensing part 3 to the wavefront sensor module 30 to convert the light signal to digital signal; (v) processing the digital signal obtained in the processor 40 to retrieve phase data; (vi) sending phase data for input to the phase correction driver 21; (vii) providing by the phase correction driver 21 reverse phase data to the phase corrector 20; (viii) correcting position of a surface by the phase corrector 20, thereby changing the wavefront of the incoming light beam; fix} wherein processing the signal obtained in the processor 40 to form phase data at the step (v) comprises the following steps: (a) digitizing images formed at the image sensor 37, (b) extracting intensity images of diffraction patterns or individual PSFs from the intensified images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations; (c) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values; (d) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase matrix data; (e) removing noises and retrieval artefacts from the obtained phase matrix data; (f) extrapolating phase data (e.g. by cubic equation) and phase surface from the phase matrix data obtained at previous step.

The number of the regions of interest corresponds to the number of the light beams 5, 6 can be divided by the beam splitters 32, 33 and originating from the wavefront sensing part 3 input into the wavefront sensor 30.

One of the preferred embodiments of the invention is shown on Fig. 1. The collimated parallel light rays coming from the optical device 1 enter the proposed optical system by means of the relay optical system and reach a wavefront phase corrector device 20. The incoming wavefront image can be selectively controlled by the phase corrector device 20. Mirror surface of the phase corrector 20 is selectively controlled by electrical signals obtained by processing the incoming image - the wavefront sensing part 3 received by the wavefront sensor 30 and transformed into signals of the phase corrector 21. In other embodiment transmissive spatial light modulation could be applied instead of deformable mirror at the phase corrector 20.

After reflection from or passing through the wavefront phase corrector 20, the light is divided into two beams by a beam splitter 11, which type may be a broadband beam splitter or spectral dichroic mirror. The light beam 2 is guided to an image or signal sensor 15, where an already corrected free of distortion image or signal is captured. The optical beam - the wavefront sensing part 3 enters the wavefront sensor module 30. The optical circuit of the wavefront sensor module 30 is described in more detail in Fig. 2. The light beam passes through the wavefront sensor module 30 equipped with a CMOS image sensor 37 (Fig. 2).

The net result of the optical arrangement given in Fig. 1 is the division of the incoming from a light source beam into (i) the reference wavefront part 2 and (ii) the wavefront sensing part 3. The device and process described is dedicated to processing by wavefront sensor 30 of the signal obtained from the wavefront sensing part 3 and providing a correcting signal to the phase corrector 20.

Figure 2 shows the principle of the optical organization of the wavefront sensor 30. The main incoming beam 3 passes through a collimation telescope 31 and afterwards is divided into two beams by means of a beam splitter 32. The divided beams are further divided according to a similar principle and necessity. The basic design shows a division into two beams, but the number may be higher depending on the application of the wavefront sensor and the required sensitivity of phase estimation. The rays coming from the beam splitters 32 and 33, which can act also as mirrors, on the pseudorandom amplitude masks 36. The number and arrangement of the masks 36 correspond to the physical arrangement of the beams. The masks 36 can be arranged in a row or in a matrix, or both. After the beam passes the amplitude masks 36, the diffraction patterns are focused by an optical system 34 on the image sensor 37, which can be any sensory device, including CCD, CMOS or other known means adapted to convert the light intensity signal to electrical and further digital form. The result achieved is a group of images 60, in which the number of elements depends on the number of amplitude masks 36 and rays 5, 6, ... n in the optical system.

The amplitude pseudorandom mask is supposed to have only amplitude information, with negligible changes of phase information. It is characterized by a randomized set of square units, those size is set to satisfy the sampling by the pixel size of the image sensor 37, according to discrete Fourier transform equations. To relate the wavefront sensor image sensor with mask parameters, every pixel size p of the image sensor 37, can be expressed in angular form taken form the optical axis. The angle 0 of pixel n is given by

0 = tan-¹ [1],

where f is a focal distance of optical system 34. The diffraction angle 6 , wavelength , and spatial frequency v are related by an equation sin(#) = -y (2)

By joining equations (1) and (2) equation is found that relates parameters of optical system, image sensor pixel size p and mask square cell P for the most distant pixel Umax: sintan-¹ [31

In the present embodiment masks are produced by lithography means, providing adhesion of metal to glass screen and subsequent photo activated etching process. [17] Total size of the individual mask corresponds to the diameter of the beams 15 and 16. The area or beam traversing through the mask might be square of round, as given in figure 5 incorporating individual cells P and transparent gaps of same size P.

The image processing scheme is given in figures 3 and 4. The group of digital intensity images coming from the image sensor 37 [Fig. 2) is normalized, initially processed, prepared for phase recovery. The necessary morphological and image processing is performed. To reconstruct the wavefront phase from the diffraction scene, which is perceived as an intensity image, a phase recovery algorithm is used [Fig. 3). Based on the properties of the coded masks 36 and light intensity measurements, the phase parameters are recovered and sent for further processing. The obtained phase information is converted into Zernike coefficients applicable to the phase corrector 20. The surface of the phase corrector 20 is controlled through the phase corrector 20. Changing the phase corrector surface or transmittance parameters changes the wavefront of the incoming beam from the optical device 1 and the telescope 31. In the process of phase reconstruction from the intensity images the respective mathematical algorithms are applied. First, the intensity images of diffraction patterns or individual PSFs are extracted from the image in the designed size to regions of interest (ROI) - Fig. 4. At this stage regions of interest (ROIs) are defined according to pre-calibrated pixel locations. Number or ROIs corresponds to the number of divided beams originating from the input beam 3 in the wavefront sensor 30. After ROIs extraction, noise levels and peak magnitudes are identified. In pre-processing stage 61 ROIs noise is processed and intensity values are feed into the phase retrieval algorithm 45 (Fig. 3). The mathematical phase retrieval algorithm 62, using adapted non-convex optimization task approach (Fourier transformation) for the phase recovery of the optical signal from intensity measurements.

General form of Gerchberg-Saxton phase retrieval can be written algorithmically: Input: Fourier magnitude-squared (amplitude) measurements y. Output: Estimate x' of the underlying signal.

Initialize: Choose a random input signal xo;

A: Inverse Fourier Transform (y)

Continue while error criterion is not satisfied

B := Amplitude(Source) x exp(i x Phase(A))

C := Fourier Transform(B)

D := Amplitude (Target) x exp(i x Phase(C)) A := 1FT(D)

Loop breaks when criterion is satisfied.

Retrieved phase = Phase(A).

The non-convex adaptive gradient descent contains two steps: (i) initialization stage is provided by weighted calculation of the sequential subset of measurements. The loop stage is similar to Gerchberg-Saxton algorithm [18]. Depending on the results of algorithm convergence success, which is a subject to noise levels and signal no noise ratio, Fienup algorithm [19] is applied interchangeably. To provide the stability of the retrieval, number of sequential retrievals are utilized and fed as initialization to the phase retrieval algorithm in the next iteration. After reconstruction of the signal, phase information is extracted, noise provided is extracted and phase is unwrapped, prepared for wavefront correction purposes at the phase corrector driver 21 (Fig. 3).

The phase postprocessing 46 is removing noises and retrieval artefacts, discontinuities and reforming phase data for input to the phase corrector driver 21. Phase angle information is extracted and processed. Depending on number of sub-rays in the wavefront sensor 30 and parameters of the amplitude masks 36 different noise levels are obtained in the phase retrieval 45 output phase data. Noise artefacts are indexed as outliers and removed from the phase matrix data. Phase data is extrapolated and final phase surface obtained.

To ensure the wavefront correction by phase corrector (DM or SLM) feedback loop operates in gradient descent approach and applies additional signal of each phase retrieval iteration to obtain the minimal error of compensation for present wavefront.

Before input to the wavefront corrector driver 21 phase data 46 is resized according to particular phase corrector, either deformable mirror or spatial light modulator, parameters - size, arrangement and number of actuators. If necessary, phase matrix data is transformed into array or vector, as provided by the phase corrector 20 manufacturer.

Since operation of the proposed device may require several beams and they have to be captured with an image matrix using an optical circuit, it can be implemented in at least three several ways.

First - using multiple image sensors 37 that capture diffraction scenes from multiple masks 36. For example, the device may comprise two masks 36 and two cameras, respectively. This principle can be multiplied to a larger number of nodes - four, six, eight and so on. Second - using a one-image sensor 37 to which images of multiple masks are directed. In this case, the number of masks 36 cannot be increased to large numbers. The optimal solution includes two and four beams, in special cases up to eight beams.

Third - using two image sensors 37, but one mask 36. The light that passes through the mask 36 forms the first beam and the reflected light forms the second beam. The number of such nodes may also be increased. In this case, part of the light that is reflected is not lost.

Depending on the number of beams utilized, the spatial arrangement of the rays can be in a row (horizontally, vertically) or in another geometry (triangular, quadrilateral, hexagonal, etc.).

In the general case, the method is applicable to the determination of the phase of any weak optical signal with the possibility to introduce real-time turbulence, temperature introduced distortion correction. The described system is adaptable to telescopes and microscopy systems. In this case, the device is mounted at the exit aperture of the telescope and is located between the telescope and the astrophotography or spectroscopy device, without affecting the operation of the optical instrument itself.

References

1. Akondi Vyas, M B Roopashree, B R Prasad. Optimization of Existing Centroiding Algorithms for Shack Hartmann Sensor. Proceeding of the National Conference on Innovative Computational Intelligence & Security Systems Sona College of Technology, Salem. Apr 3-4, 2009. pp 400-405.

2. Wang, C., Dun, X., Fu, Q., Heindrich, W. (2017) Ultra-high resolution coded wavefront sensor. Optics Express, 25(12), pp.13736-13746.

3. Wang, C., Fu, Q., Dun, X., Heindrich, W. (2018) Megapixel adaptive optics: towards correcting large-scale distortions in computational cameras. ACM Trans. Graph., 37(4), pp.115:1-115:12.

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Claims

Claims

1. An optical system for controlling optical aberrations incorporating coded patterns, comprising: a wavefront phase corrector device (20); a beam splitter (11); an image or signal sensor (15); a wavefront sensor module (30), comprising a signal processor (40); a phase correction driver (21), electrically connected with the processor (40) and the wavefront phase corrector (20); the phase corrector (20) is designed to be able to receive a light beam from a light beam source and controllably optically transfer the light beam to the beam splitter (11); the beam splitter (11) is designed to split the light beam received into two optical beams: the original wavefront part (2) and the wavefront sensing part (3), as well as optically send the original wavefront part (2) of the light beam to the image or signal sensor (15) and the wavefront sensing part (3) of the light beam - to the wavefront sensor module (30); the wavefront sensor module (30) comprising the processor (40), a collimation telescope (31); one or more beam splitters (32, 33, ...), optically connected to the collimation telescope (31) and adapted to split the light beam received from the telescope (31) into two optical beams; one or more amplitude masks (36), adapted to produce diffraction patterns; an optical system (34); and image sensor (37), adapted to convert the light intensity signal to digital; the beam splitters (32, 33, ...) are further adapted to optically send the light beam (5, 6) through the amplitude masks (36) to the optical system (34), where the optical system (34) is adapted to optically focus diffraction patterns produced by the masks (36), which are optically received from the beam splitters (32, 33, ...), on the image sensor (37); wherein the processor (40) comprises instructions for

(a) digitizing images formed at the image sensor (37),

(b) extracting intensity images of diffraction patterns or individual PSFs from the digitized images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations;

(c) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values; (d) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase matrix data;

(e) removing noises and retrieval artefacts from the obtained phase matrix data;

(f) extrapolating phase data and phase surface from the phase matrix data obtained at previous step.

2. The optical system according to claim 1, wherein the amplitude masks (36) and the divided beams (5, 6, ...) are spatially arranged in a row, or a matrix.

3. The optical system according to claim 1, wherein the image sensor (37) is a CMOS image sensor or a CCD image sensor.

4. The optical system according to claim 1, wherein the phase corrector (20) comprises a deformable mirror or a spatial light modulator.

5. A process for controlling optical aberrations incorporating coded patterns, comprising the following steps:

(i) providing a light beam to a phase corrector (20);

(ii) directing light from the phase corrector (20) to a beam splitter (11);

(hi) splitting the light beam in the beam splitter (11) into two optical beams: theoriginal wavefront part (2) and the wavefront sensing part (3);

(iv) directing the reference wavefront light beam part (2) to an image or signal sensor (15), directing the wavefront sensing part (3) to the wavefront sensor module (30) to convert the light signal to digital signal;

(v) processing the digital signal obtained in the processor (40) to retrieve phase data;

(vi) sending phase data for input to the phase correction driver (21);

(vii) providing by the phase correction driver (21) reverse phase data to the phase corrector (20);

(viii) correcting position of a surface by the phase corrector (20), thereby changing the wavefront of the incoming light beam; 17 wherein processing the signal obtained in the processor (40) to form phase data at the step (v) comprises the following steps:

(a) digitizing images formed at the image sensor (37),

(b) extracting intensity images of diffraction patterns or individual PSFs from the digitized images in the regions of interest; where regions of interest are defined according to pre-calibrated pixel locations;

(c) identifying noise levels and peak magnitudes in the extracted images and obtaining intensity values;

(d) performing Fourier based phase retrieval of the intensity values obtained to retrieve phase matrix data;

(e) removing noises and retrieval artefacts from the obtained phase matrix data;

(f) extrapolating phase data and phase surface from the phase matrix data obtained at previous step.

6. The process according to claim 5, wherein the number of the regions of interest corresponds to the number of the light beams (5, 6) divided by the beam splitters (32, 33) and originating from the wavefront sensing part (3) input into the wavefront sensor (30).