CN113091644B - Large-aperture optical element surface shape detection method based on stacked coherent diffraction imaging - Google Patents
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Abstract
The invention discloses a surface shape detection method of a large-aperture optical element based on stacked coherent diffraction imaging, which relates to the technical field of optical detection and digital image processing, solves the technical problem of small measurement field of view in the existing stacked coherent diffraction imaging technology, realizes the surface shape measurement of the large-aperture optical element, and comprises the following steps: moving the element to be measured to the initial sub-aperture scanning position and aligning; collecting diffraction light spots by a camera; translating the element to be measured to the next sub-aperture scanning position and collecting diffraction light spots, wherein the sub-apertures of adjacent sub-aperture scanning positions need to have a certain overlapping area; until the scanning sub-aperture light spot covers the area to be measured of the optical element; processing the collected series of diffraction images, and recovering the surface shape distribution of the element to be detected by adopting a laminated coherent diffraction imaging iterative algorithm; the invention is used for detecting the surface shape of the large-caliber optical element and has the advantages of large caliber, simple optical path and low cost.
Description
Technical Field
The invention relates to the technical field of optical detection and digital images, in particular to the technical field of a large-aperture optical element surface shape detection method based on stacked coherent diffraction imaging, which is used for detecting the surface shape of a large-aperture optical element.
Background
In the process of free space propagation of the optical field, the complex amplitude of the optical field changes due to the diffraction effect of light. According to the Fresnel diffraction principle, if the complex amplitude distribution of the light field at a certain position is known, the complex amplitude distribution of the light field after the light field propagates for a certain distance can be calculated under the paraxial condition. If only the intensity distribution of the light field is known, theoretically, the intensity distribution of the light field at two positions along the optical axis direction needs to be known, and the phase distribution of the light field can be solved by adopting an iterative algorithm based on light field diffraction propagation, which is the basic principle of coherent diffraction imaging.
The laminated coherent diffraction imaging is widely applied to the field of biological imaging, and the amplitude and phase distribution of the biological sample can be restored by performing sub-aperture scanning measurement on the biological sample and performing iterative operation on each sub-aperture image. Due to the overlapping area among the sub-apertures, the information redundancy can lead the result iteration convergence to approach the real light field distribution of the sample. In the field of biological imaging, the conventional laminated coherent diffraction imaging sub-aperture field of view is generally only millimeter-scale, and the measurement of objects with the size of hundreds of millimeters is difficult to realize.
The interferometer is used for measuring the surface shape of the optical element, and is a mature measuring means at the present stage. Aiming at a large-caliber optical element, an interferometer with a corresponding caliber is generally matched to realize full-caliber measurement; if a small-caliber interferometer is used for measuring a large-caliber element, sub-aperture splicing measurement needs to be carried out, and extra measurement errors are introduced in the splicing process. The large-aperture interferometer is expensive and has high requirements on environmental vibration, temperature and the like. In order to reduce stress deformation caused by the gravity of the standard mirror, the interferometer with the caliber of 300mm or more adopts a horizontal light path, and the element to be measured is vertically placed. The large-aperture interferometer is difficult to measure the surface shape of an optical element placed at a pitching angle.
Disclosure of Invention
The invention aims to: the invention provides a large-aperture optical element surface shape detection method based on stacked coherent diffraction imaging, and aims to realize surface shape measurement of a large-aperture optical element at a pitch angle and solve the technical problem of small measurement field of view in the existing stacked coherent diffraction imaging technology.
The invention specifically adopts the following technical scheme for realizing the purpose:
a surface shape detection method for a large-aperture optical element based on stacked coherent diffraction imaging is characterized in that an element to be detected is located at a parallel light position after beam expansion and collimation, and the aperture of the parallel light is limited by the aperture of a collimating lens. The aperture of the general collimating lens can be 100 mm-200 mm by comprehensively considering the factors of measuring efficiency, lens processing difficulty and cost. The method comprises the following steps:
step 1, moving an element to be measured to an initial sub-aperture scanning position and aligning, and collecting a diffraction light spot image near a convergent light focus by using a camera;
step 2, translating the element to be measured to the next sub-aperture scanning position and collecting diffraction light spot images corresponding to the sub-aperture scanning position, wherein adjacent sub-apertures have overlapping areas; the element to be tested can realize translation scanning by adopting a two-dimensional guide rail or a moving device such as a mechanical arm and the like;
step 3, repeating the step 2 until all diffraction light spot images collected at the sub-aperture scanning positions cover the area to be measured of the optical element to be measured;
and 4, processing the series of diffraction spot images acquired by the optical element to be detected, and recovering the surface shape distribution of the optical element to be detected by adopting a laminated coherent diffraction imaging iterative algorithm.
Further, in step 4, the concrete steps of recovering the surface shape distribution of the element to be measured are as follows:
step a, setting the initial distribution P of the complex amplitude of the detection light field and the initial value O of the surface shape distribution of the element to be detected;
step b, setting the wave front reflected by the element to be measured as Uj(r)＝2Pj·Oj(r)，
In the formula of Uj(r) is the reflected wavefront through the jth iteration of the sub-aperture at the position r of the element to be measured, Oj(r) is the surface shape value of the jth iteration of the sub-aperture at the r position of the element to be measured, PjThe complex amplitude distribution after the jth iteration of the detection light field is obtained;
step c, light field complex amplitude at the position of the camera target surface
The Fresnel diffraction formula or the Coriolis formula is adopted for calculation, and the Fresnel diffraction calculation formula is as follows:
in the formula, Vj(r) is the light field complex amplitude at the camera target surface of the jth iteration of the sub-aperture at the position of the element to be measured r,
representing a diffractive transmission process, UjFor the wavefront after the jth iterative reflection from the device under test, U (x)0,y0) The complex amplitude distribution of the object plane light field is obtained, the complex amplitude distribution of the image plane light field is obtained after V (x, y) diffraction transmission, lambda is the wavelength of measurement light, and d is the diffraction transmission distance between an image plane and an object plane;
d, according to the actual light intensity distribution I (r) collected by the camera, comparing V in the step cj(r) updating, replacing amplitude and preserving phase, cameraComplex amplitude of light field after jth iteration update at target surface
In the formula, I (r) is the light intensity actually collected by the camera at the position of r of the element to be measured at the aperture;
step e, comparing V 'in step d'j(r) performing inverse diffraction propagation to calculate the wavefront at the device under test
In formula (II) U'j(r) is the complex amplitude of the wave front calculated by the inverse diffraction propagation after the jth iteration at the element to be measured,
representing a diffractive reverse transport process; the formula of the Fresnel diffraction calculation of the diffraction reverse transmission is as follows:
wherein V (x, y) is the complex amplitude distribution of the image plane light field, and U (x)0,y0) After diffraction reverse transmission, the complex amplitude distribution of the object plane light field is realized, wherein lambda is the wavelength of measuring light, and d is the diffraction transmission distance between the image plane and the object plane;
f, updating the surface shape distribution of the element to be detected with the sub-aperture at the r position, updating the complex amplitude distribution of the detection light field with the sub-aperture at the r position after the surface shape distribution of the element to be detected is contoured (the detection light can be updated after the general iteration number j is more than or equal to 10), and then calculating a recovery error;
the formula for updating the surface shape distribution of the element to be measured is as follows:
the formula for detecting the update of the light field complex amplitude distribution is as follows:
calculating a recovery error formula:
wherein r is the position of the sub-aperture of the device to be measured, PjFor the detection of the complex amplitude distribution of the light field for the j-th iteration, Pj' detection light field complex amplitude distribution for updated j-th iteration, P* jIs PjConjugate of (1, | P)j|maxIs PjMaximum value of the modulus value of (a); o isj(r) is a face value, O ', of the jth iteration of the sub-aperture at the position of the element to be measured r'j(r) updating a postamble value for the jth iteration,
is OjConjugation of (r), | Oj(r)|maxIs Oj(r) maximum value of modulus value; u shapej(r) is the wavefront, U ', after reflection of the jth iteration of the sub-aperture at the location of the element under test r'j(r) updated j-th iteration of the reflected wavefront, Vj(r) is the complex amplitude of the light field at the camera target surface of the jth iteration of the sub-aperture at the r position of the element to be detected, I (r) is the light intensity actually acquired by the camera at the sub-aperture at the r position of the element to be detected, and E is the recovery error;
and h, moving the detection light to the r +1 position sub-aperture, and repeating the steps b to f until the recovery error is converged to be smaller than a set value, thereby completing the recovery of the surface shape distribution of the element to be detected.
The invention has the following beneficial effects:
by scanning the optical element at the large aperture beam position, the measurement range can be extended. The aperture of a single scanning sub-aperture can reach hundreds of millimeters, and the method is suitable for wavefront measurement of large-aperture optical elements and theoretically can measure optical elements with meter-level dimensions. The device has the advantages of simple measuring light path, large view field and high precision.
Drawings
FIG. 1 is a schematic view of a measurement optical path according to the present invention;
FIG. 2 is a schematic view of a neutron aperture scan during a measurement process of the present invention;
FIG. 3 is a simulated surface profile distribution of a device under test according to the present invention;
FIG. 4 is a diagram showing the distribution of diffracted light received by the camera according to the present invention;
FIG. 5 shows the intensity distribution and phase distribution of the recovered detection light in the present invention;
FIG. 6 is a diagram illustrating the recovered surface profile of the DUT in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Example 1
As shown in fig. 1 and 2, in a method for detecting a surface shape of a large-aperture optical element based on stacked coherent diffraction imaging, an element to be detected is located at a parallel light position after beam expansion and collimation, and the aperture of the parallel light is limited by the aperture of a collimating lens. The aperture of the general collimating lens can be 100 mm-200 mm by comprehensively considering the factors of measuring efficiency, lens processing difficulty and cost. The method comprises the following steps:
step 1, moving a component to be measured to an initial sub-aperture scanning position and aligning, and collecting a diffraction light spot image of the initial sub-aperture scanning position by using a camera;
step 2, translating the element to be tested to the next sub-aperture scanning position and collecting diffraction light spot images corresponding to the sub-aperture scanning position, wherein adjacent sub-apertures have overlapping areas, and the element to be tested can realize translation scanning by adopting a two-dimensional guide rail or a mechanical arm and other moving devices;
step 3, repeating the step 2 until all the diffraction light spot images collected at the sub-aperture scanning positions cover the area to be measured of the optical element to be measured;
and 4, processing the series of diffraction spot images acquired by the optical element to be detected, and recovering the surface shape distribution of the optical element to be detected by adopting a laminated coherent diffraction imaging iterative algorithm.
In step 4, the concrete steps of recovering the surface shape distribution of the element to be detected are as follows:
step a, setting the initial distribution P of the complex amplitude of the detection light field and the initial value O of the surface shape distribution of the element to be detected;
step b, setting the wave front reflected by the element to be measured as Uj(r)＝2Pj·Oj(r)，
In the formula of Uj(r) is the reflected wavefront through the jth iteration of the sub-aperture at the position r of the element to be measured, Oj(r) is the surface shape value of the jth iteration of the sub-aperture at the r position of the element to be measured, PjThe complex amplitude distribution after the jth iteration of the detection light field is obtained;
step c, light field complex amplitude at the position of the camera target surface
The Fresnel diffraction formula or the Coriolis formula is adopted for calculation, and the Fresnel diffraction calculation formula is as follows:
in the formula, Vj(r) is the light field complex amplitude at the camera target surface of the jth iteration of the sub-aperture at the position of the element to be measured r,
representing a diffractive transmission process, UjFor the wavefront after the jth iterative reflection from the device under test, U (x)0,y0) The complex amplitude distribution of the object plane light field is obtained, the complex amplitude distribution of the image plane light field is obtained after V (x, y) diffraction transmission, lambda is the wavelength of measurement light, and d is the diffraction transmission distance between an image plane and an object plane;
d, according to the actual light intensity distribution I (r) collected by the camera, comparing V in the step cj(r) updating the amplitudeReplacing and retaining the phase, the complex amplitude of the light field after the jth iterative update at the target surface of the camera
In the formula, I (r) is the light intensity actually collected by the camera at the position of r of the element to be measured at the aperture;
step e, comparing V 'in step d'j(r) performing inverse diffraction propagation to calculate the wavefront at the device under test
In formula (II) U'j(r) is the complex amplitude of the wave front calculated by the inverse diffraction propagation after the jth iteration at the element to be measured,
representing a diffractive reverse transport process; the formula of the Fresnel diffraction calculation of the diffraction reverse transmission is as follows:
wherein V (x, y) is the complex amplitude distribution of the image plane light field, and U (x)0,y0) After diffraction reverse transmission, the complex amplitude distribution of the object plane light field is realized, wherein lambda is the wavelength of measuring light, and d is the diffraction transmission distance between the image plane and the object plane;
f, updating the surface shape distribution of the element to be detected with the sub-aperture at the r position, updating the complex amplitude distribution of the detection light field with the sub-aperture at the r position after the surface shape distribution of the element to be detected is contoured (the detection light can be updated after the general iteration number j is more than or equal to 10), and then calculating a recovery error;
the formula for updating the surface shape distribution of the element to be measured is as follows:
the formula for detecting the update of the light field complex amplitude distribution is as follows:
calculating a recovery error formula:
wherein r is the position of the sub-aperture of the device to be measured, PjIs the detected light field complex amplitude distribution of the j iteration, P'jFor updated complex amplitude distribution of the detected light field for the j-th iteration, P* jIs PjConjugate of (1, | P)j|maxIs PjMaximum value of the modulus value of (a); o isj(r) is the surface shape value of j iteration of sub-aperture at r position of the element to be measured, Oj' (r) update the trailing profile value for the jth iteration,
is OjConjugation of (r), | Oj(r)|maxIs Oj(r) maximum value of modulus value; u shapej(r) is the wavefront, U ', after reflection of the jth iteration of the sub-aperture at the location of the element under test r'j(r) updated j-th iteration of the reflected wavefront, Vj(r) is the complex amplitude of the light field at the camera target surface of the jth iteration of the sub-aperture at the r position of the element to be detected, I (r) is the light intensity actually acquired by the camera at the sub-aperture at the r position of the element to be detected, and E is the recovery error;
and h, moving the detection light to the r +1 position sub-aperture, and repeating the steps b to f until the recovery error is converged to be smaller than a set value, thereby completing the recovery of the surface shape distribution of the element to be detected.
Example 2
The embodiment provides a method for iteratively and automatically extracting a center of a cross graph based on least square fitting, which comprises the following steps:
step 1, moving a component to be measured to an initial scanning position and aligning; the simulated surface profile distribution of the device to be measured in this embodiment is shown in fig. 3, where the device size is 400mm × 400mm, the device surface profile PV is 0.5 λ (λ ═ 632.8nm), and the aperture of the measuring beam is 100 mm.
Step 2, collecting diffraction light spots by a camera; the simulated camera of this embodiment has a pixel resolution of 1000 × 1000 and a pixel size of 5 μm.
Step 3, translating the element to be measured to the next scanning position and collecting diffraction light spots, wherein the sub-apertures of the adjacent scanning positions need to have a certain overlapping area; the ratio of the area of the overlapping region to the area of the sub-aperture is 60%.
Step 4, repeating the step 2 and the step 3 until the scanning sub-aperture light spot covers the area to be measured of the optical element; the collected patterns of adjacent 4 diffraction spots are shown in FIG. 4.
And 5, processing the collected series of diffraction images, and recovering the surface shape distribution of the element to be detected by adopting a laminated coherent diffraction imaging iterative algorithm. The restored detection light intensity distribution and phase distribution are shown in fig. 5, and the restored surface profile distribution of the device under test is shown in fig. 6.
Claims (1)
1. A large-aperture optical element surface shape detection method based on stacked coherent diffraction imaging is characterized by comprising the following steps:
step 1, moving a component to be measured to an initial sub-aperture scanning position and aligning, and collecting a diffraction light spot image of the initial sub-aperture scanning position by using a camera;
step 2, translating the element to be tested to the next sub-aperture scanning position and collecting diffraction light spot images corresponding to the sub-aperture scanning position, wherein adjacent sub-apertures have overlapping areas, and the element to be tested adopts a moving device to realize translation scanning;
step 3, repeating the step 2 until all the diffraction light spot images collected at the sub-aperture scanning positions cover the area to be measured of the optical element to be measured;
step 4, processing the series of diffraction spot images collected by the optical element to be detected, and recovering the surface shape distribution of the optical element to be detected by adopting a laminated coherent diffraction imaging iterative algorithm;
in step 4, the concrete steps of recovering the surface shape distribution of the element to be detected are as follows:
step a, setting the initial distribution P of the complex amplitude of the detection light field and the initial value O of the surface shape distribution of the element to be detected;
step b, setting the wave front reflected by the element to be measured as Uj(r)＝2Pj·Oj(r)，
In the formula of Uj(r) is the reflected wavefront through the jth iteration of the sub-aperture at the position r of the element to be measured, Oj(r) is the surface shape value of the jth iteration of the sub-aperture at the r position of the element to be measured, PjThe complex amplitude distribution after the jth iteration of the detection light field is obtained;
step c, light field complex amplitude at the position of the camera target surface
Calculating by using Fresnel diffraction formula or Coriolis formula, wherein Vj(r) is the light field complex amplitude at the camera target surface of the jth iteration of the sub-aperture at the position of the element to be measured r,
representing a diffractive transmission process, UjThe wave front is the wave front after the jth iterative reflection of the element to be tested;
d, according to the actual light intensity distribution I (r) collected by the camera, comparing V in the step cj(r) updating, replacing the amplitude and reserving the phase, and iteratively updating the j th time of the complex amplitude of the light field at the target surface of the camera
In the formula, I (r) is the light intensity actually collected by the camera at the position of r of the element to be measured at the aperture;
step e, comparing V 'in step d'j(r) performing inverse diffraction propagation to calculate the wavefront at the device under test
In formula (II) U'j(r) is the complex amplitude of the wave front calculated by the inverse diffraction propagation after the jth iteration at the element to be measured,
representing a diffractive reverse transport process;
f, updating the surface shape distribution of the element to be detected with the sub-aperture at the r position, updating the complex amplitude distribution of the detection light field with the sub-aperture at the r position after the surface shape distribution of the element to be detected is contoured, and then calculating a recovery error;
the formula for updating the surface shape distribution of the element to be measured is as follows:
the formula for detecting the update of the light field complex amplitude distribution is as follows:
calculating a recovery error formula:
wherein r is the position of the sub-aperture of the device to be measured, PjIs the detected light field complex amplitude distribution of the j iteration, P'jFor updated complex amplitude distribution of the detected light field for the j-th iteration, P* jIs PjConjugate of (1, | P)j|maxIs PjMaximum value of the modulus value of (a); o isj(r) is a face value, O ', of the jth iteration of the sub-aperture at the position of the element to be measured r'j(r) updating a postamble value for the jth iteration,
is OjConjugation of (r), | Oj(r)|maxIs Oj(r) maximum value of modulus value; u shapej(r) is the wavefront, U ', after reflection of the jth iteration of the sub-aperture at the location of the element under test r'j(r) updated j-th iteration of the reflected wavefront, Vj(r) for j iterations of sub-apertures at the r position of the element to be measuredThe complex amplitude of the light field at the target surface of the camera, I (r) is the light intensity actually acquired by the camera at the sub-aperture of the element to be detected at the position r, and E is the recovery error;
and h, moving the detection light to the r +1 position sub-aperture, and repeating the steps b to f until the recovery error is converged to be smaller than a set value, thereby completing the recovery of the surface shape distribution of the element to be detected.
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