Method and device for selecting transverse shearing interference shearing rate

Abstract

The invention discloses a lateral shear interference shear rate selection method and device, and relates to the technical field of optical measurement. The method is used for solving the problems that stripes cannot be analyzed and the detection precision is limited due to random or non-theoretical-reference shearing rate selection when a transverse shearing interference method is used for multi-type aspheric surface shape universal detection. Comprising the following steps: according to a radius iteration range of an initial reference curved surface, in each first iteration step length, according to an iteration range of an initial shearing rate, sequentially confirming a transverse shearing interference pattern fringe density corresponding to the initial shearing rate under a second iteration step length, when a maximum transverse shearing interference pattern fringe density in the plurality of transverse shearing interference pattern fringe densities is smaller than a maximum analysis threshold value of actual interference fringes, obtaining a coarse optimization shearing rate, a first range of the coarse optimization shearing rate and a radius of an optimal reference curved surface; and under each third iteration step length, when it is determined that the average fringe density of the lateral shearing interferogram is smaller than the judgment condition, a fine optimization shearing rate is obtained, and the fine optimization shearing rate is in a first range.

Description

Technical Field

[0001] The present invention relates to the field of optical measurement technology, and more specifically to a method and device for selecting a transverse shear interference shear rate. Background Art

[0002] The application of lateral shearing interferometry in the field of aspheric surface shape measurement has the advantages of being resistant to environmental interference, introducing no reference mirror error, and improving the problem of fringe densification caused by asphericity. Due to the rich changes in aspheric wavefronts, when using a single shear amount to measure multiple types of aspheric surface shapes, there may be problems such as fringes that are too dense to be resolved or fringes that are too sparse and lack phase sensitivity. Therefore, the appropriate shear rate should be matched for the measurement of multiple types of aspheric wavefront changes, so as to better ensure the measurement accuracy of the aspheric surface shape.

[0003] In the prior art, when addressing the detection problem of multiple types of aspheric surfaces, only the calibration of shear rate and shear amount in lateral shearing interferometry is considered, while the adaptive selection method of shear rate is not considered; compared with the adaptive wavefront sensor mentioned in the document "Integrated diffractive shearing interferometry for adaptive wavefront sensing" by Jason H. Karp et al. in 2008, it only preliminarily mentioned the influence of signal-to-noise ratio and wavefront slope on shear rate selection, but did not provide a specific theoretical model and data support; compared with the lateral shear aspheric measurement method mentioned in the document "Double grating phase stepping interferometry for testing aspherics" by Jean-Pierre Betend-Bon et al. in 1991, it only provided a lateral shear aspheric measurement device, and did not describe the influence of the wavefront change of the aspheric surface to be measured on the shear rate selection.

[0004] None of the above-mentioned related technologies have proposed a method for adaptively optimizing the selection of shear rate for the aspheric wavefront to be measured. The reason is that before the emergence of new shearing methods, the traditional lateral shearing interference measurement method could not achieve precise and controllable adjustment of the shear rate. Therefore, the relevant research and technology for adaptively selecting the shear rate according to the aspheric wavefront parameters have not been mentioned. In the past two years, with the emergence of methods for achieving precise and controllable shear rates, it has become possible to adaptively adjust the shear rate for multiple types of aspheric wavefronts. Therefore, it is urgent to carry out relevant research on the technology of adaptive optimal shear rate selection for aspheric wavefronts to promote the rapid development of lateral shearing interference aspheric measurement technology. Summary of the invention

[0005] The embodiments of the present invention provide a method and device for selecting shear rate of lateral shearing interference, which are used to solve the problem of unresolvable fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection when using the lateral shearing interference method for universal detection of multiple types of aspheric surfaces.

[0006] The embodiment of the present invention provides a method for selecting a lateral shear interference shear rate, comprising:

[0007] Determining the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function;

[0008] According to the iteration range of the radius of the initial reference surface, the first iteration step of the radius of the initial reference surface is determined; within each of the first iteration step, according to the iteration range of the initial shear rate and the second iteration step of the initial shear rate, the lateral shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step is confirmed in sequence; when there is a maximum lateral shear interference pattern fringe density among the multiple lateral shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringe, a rough optimized shear rate and a first range of rough optimized shear rates matching the iteration range of the radius are obtained; according to the maximum rough optimized shear rate included in the first range of rough optimized shear rates, the radius of the optimal reference surface is obtained;

[0009] According to the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate, at each third iterative step, the average fringe density of the lateral shear interference pattern is determined in sequence according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the lateral shear interference pattern is less than the judgment condition, the fine optimized shear rate and the first range of the fine optimized shear rate matching the first range of the coarse optimized shear rate are obtained according to the average fringe density of the lateral shear interference pattern.

[0010] Preferably, when there is a maximum lateral shearing interference pattern fringe density that is less than the maximum analytical threshold of the actual interference fringe, the rough optimized shear rate is obtained by the following formula:

[0011]

[0012] Wherein, Max[Density] represents the maximum lateral shearing interference pattern fringe density among the plurality of lateral shearing interference pattern fringe densities, and Density max Indicates the maximum resolvable threshold of the actual interference fringes, Ratio 1 represents the rough optimal shear rate, D aspheric represents the aperture of the aspheric surface to be measured, q represents the pixel size of the detector target surface, and y direpresents the ordinate of a point D on the aspherical surface to be measured, represents the iteration range of the initial shear rate and λ represents the wavelength.

[0013] Preferably, the rough optimized shear rate and the first range of the rough optimized shear rate matching the radius iteration range are obtained by the following formula:

[0014]

[0015] Among them, Ratio max represents the first range of the rough optimized shear rate matching the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rate, r 1 Indicates the radius of the best reference surface.

[0016] Preferably, the judgment condition is that the average fringe density of the lateral shearing interference pattern is less than 50 pixels / strip;

[0017] When it is determined that the average fringe density of the lateral shearing interference pattern is less than the judgment condition, the fine optimized shearing rate and the first range of the fine optimized shearing rate matching the first range of the coarse optimized shearing rate are obtained by the following formula:

[0018]

[0019] Among them, Density average represents the average fringe density of the lateral shearing interferogram, M represents the number of bright fringes in the lateral shearing interference pattern, Ratio 2 Indicates the optimized shear rate, ratio 1 represents the rough optimized shear rate, Represents the value range of the first range of the rough optimized shear rate.

[0020] Preferably, the step of sequentially determining the fringe density of the transverse shearing interference pattern corresponding to the initial shear rate under the second iteration step size specifically includes:

[0021] The shearing amount is determined by the following formula according to the aperture and initial shear rate of the aspheric surface to be tested:

[0022] S=ratio 0 *D aspheric

[0023] According to the aspheric surface to be measured, the initial reference curved surface, the vertex curvature radius R of the aspheric surface to be measured 0 And the shear amount is determined by the following formula to determine the center point position of the lateral shear interference bright fringe:

[0024]

[0025] The lateral shearing interference pattern fringe density matching the initial reference surface is determined by the following formula according to the center point positions of two adjacent lateral shearing interference bright fringes:

[0026]

[0027] Where S represents the shear amount, Ratio 0 represents the initial shear rate, D aspheric Indicates the aperture of the aspheric surface to be measured, T i represents the center position of the lateral shear interference bright fringe, r 0 represents the radius of the initial reference surface, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di Indicates the ordinate of a point D on the aspherical surface to be measured, y ci The ordinate of a point C on the initial reference surface, R 0 represents the vertex curvature radius of the aspheric surface to be measured, k represents the quadratic cone coefficient, λ represents the wavelength, and Density represents the fringe density of the lateral shearing interference pattern.

[0028] Preferably, after determining the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface, the method further comprises:

[0029] The aspheric surface to be measured is placed in a rectangular coordinate system, and the path difference between the initial reference surface and the aspheric surface to be measured is determined. The path difference is as follows:

[0030]

[0031] Among them, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di The ordinate of a point D on the aspherical surface to be measured, y ci represents the ordinate of a point C on the initial reference surface, r 0 represents the radius of the initial reference surface, Represents the tangent distance between points C and D.

[0032] The embodiment of the present invention provides a lateral shear interference shear rate selection device, comprising:

[0033] A determination unit, configured to determine the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function;

[0034] A first obtaining unit is used to determine a first iteration step of the radius of the initial reference surface according to an iteration range of the radius of the initial reference surface, and within each of the first iteration step, sequentially confirm the lateral shearing interference pattern fringe density corresponding to the initial shearing rate under the second iteration step according to the iteration range of the initial shearing rate and the second iteration step of the initial shearing rate, and when there is a maximum lateral shearing interference pattern fringe density among a plurality of the lateral shearing interference pattern fringe densities that is less than a maximum analytical threshold of the actual interference fringe, obtain a rough optimized shear rate and a first range of rough optimized shear rates that matches the iteration range of the radius; and obtain the radius of the optimal reference surface according to the maximum rough optimized shear rate included in the first range of rough optimized shear rates;

[0035] The second obtaining unit is used to determine the average fringe density of the lateral shearing interference pattern in turn according to the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate at each third iterative step according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the lateral shearing interference pattern is less than the judgment condition, the fine optimized shear rate and the first range of fine optimized shear rate matching the first range of the coarse optimized shear rate are obtained according to the average fringe density of the lateral shearing interference pattern.

[0036] Preferably, the first obtaining unit is specifically used to obtain the rough optimized shear rate by the following formula:

[0037]

[0038] The rough optimized shear rate and the first range of the rough optimized shear rate matching the radius iteration range are obtained by the following formula:

[0039]

[0040] Wherein, Max[Density] represents the maximum lateral shearing interference pattern fringe density among the plurality of lateral shearing interference pattern fringe densities, and Density max Indicates the maximum resolvable threshold of the actual interference fringes, ratio 1 represents the rough optimal shear rate, D aspheric represents the aperture of the aspheric surface to be measured, q represents the pixel size of the detector target surface, and y di represents the ordinate of a point D on the aspherical surface to be measured, represents the iteration range of the initial shear rate, λ represents the wavelength, and ratio maxrepresents the first range of the rough optimized shear rate matching the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rate, r 1 Indicates the radius of the best reference surface.

[0041] An embodiment of the present invention provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes any one of the above-mentioned lateral shear interference shear rate selection methods.

[0042] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes any one of the above-mentioned lateral shear interference shear rate selection methods.

[0043] In summary, an embodiment of the present invention provides a method and device for selecting a lateral shear interference shear rate, the method comprising: determining the vertex curvature radius of the aspheric surface to be measured as the radius of an initial reference surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function; determining a first iteration step of the radius of the initial reference surface according to an iteration range of the radius of the initial reference surface, within each of the first iteration step, according to the iteration range of the initial shear rate and the second iteration step of the initial shear rate, confirming in sequence the lateral shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step, when there is a maximum lateral shear interference pattern fringe density among a plurality of the lateral shear interference pattern fringe densities. When it is smaller than the maximum analytical threshold of the actual interference fringes, a coarse optimized shear rate and a first range of coarse optimized shear rates matching the said radius iteration range are obtained; the radius of the best reference surface is obtained according to the maximum coarse optimized shear rate included in the said first range of coarse optimized shear rates; according to the said first range of coarse optimized shear rates and the third iteration step of the coarse optimized shear rate, at each third iteration step, the average fringe density of the lateral shear interference pattern is determined in turn according to the said first range of coarse optimized shear rates and the radius of the best reference surface; when it is determined that the average fringe density of the lateral shear interference pattern is smaller than the judgment condition, the fine optimized shear rate and the first range of fine optimized shear rates matching the said first range of coarse optimized shear rates are obtained according to the said average fringe density of the lateral shear interference pattern. The method comprehensively considers the influence of factors such as the surface parameters of the aspheric surface to be tested, the fringe density of the lateral shearing interference pattern, the radius of the optimal reference surface and the actual interference pattern quality on the fringe analysis, and establishes a method for selecting a fine optimized shear rate through a coarse optimized shear rate selection theoretical model and a fine optimized shear rate selection theoretical model, wherein the coarse optimized shear rate selection theoretical model uses the fringe density of the lateral shearing interference pattern and the radius of the initial reference surface as optimization targets to determine the first range of the coarse optimized shear rate, that is, the selectable range of the coarse optimized shear rate, further, the fine optimized shear rate selection theoretical model uses the surface reconstruction accuracy as the optimization target, and further selects the fine optimized shear rate within the first range of the coarse optimized shear rate. The method provided in the embodiment of the present invention can solve the problem of unresolvable fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection when the lateral shear interference method is used for universal detection of multiple types of aspheric surfaces. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 A schematic flow chart of a method for selecting a transverse shear interference shear rate provided in an embodiment of the present invention;

[0046] Figure 2 A schematic diagram of aspheric surface and optimal reference spherical surface parameters provided by an embodiment of the present invention;

[0047] Figure 3 A schematic diagram of average stripe density provided by an embodiment of the present invention;

[0048] Figure 4 A schematic diagram of the overall process of the secondary iterative optimization adaptive shear rate selection method provided by an embodiment of the present invention;

[0049] Figure 5 A schematic structural diagram of a lateral shear interference shear rate selection device provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0051] Figure 1 A schematic flow chart of a method for selecting a lateral shear interference shear rate according to an embodiment of the present invention; Figure 1 Taking the example of FIG. 1 as an example, the method for selecting the lateral shear interference shear rate provided by the embodiment of the present invention is described in detail. Figure 1 As shown, the method comprises the following steps:

[0052] Step 101, determining the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function;

[0053] Step 102, according to the radius iteration range of the initial reference surface, determine the first iteration step of the radius of the initial reference surface, within each of the first iteration step, according to the iteration range of the initial shear rate and the second iteration step of the initial shear rate, confirm in sequence the lateral shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step, when there is a maximum lateral shear interference pattern fringe density among the multiple lateral shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringe, obtain the rough optimized shear rate and the first range of the rough optimized shear rate that matches the radius iteration range; according to the maximum rough optimized shear rate included in the first range of the rough optimized shear rate, obtain the radius of the optimal reference surface;

[0054] Step 103, based on the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate, at each third iterative step, determine in sequence the average fringe density of the lateral shear interference pattern according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface, and when it is determined that the average fringe density of the lateral shear interference pattern is less than the judgment condition, obtain the fine optimized shear rate and the first range of the fine optimized shear rate that matches the first range of the coarse optimized shear rate according to the average fringe density of the lateral shear interference pattern.

[0055] Before performing the lateral shear interference shear rate selection method in the embodiment of the present invention, it is necessary to first establish a coarse optimization shear rate selection theoretical model, an optimal reference surface radius theoretical model, and a fine optimization shear rate selection theoretical model.

[0056] Specifically, the rough optimization rate shear selection theoretical model is obtained by the following method:

[0057] In practical applications, the interference fringe position and the maximum fringe density can be determined by calculating the path difference between a series of spherical waves and aspherical waves. The aspherical wavefront function is the aspherical surface shape function to be measured, which can be expressed by formula (1):

[0058]

[0059] Where z is the rotational symmetry axis, k is the quadratic cone coefficient, and R 0 Indicates the vertex curvature radius of the aspheric surface to be measured, A 4 , A 6 , ..., A 2n represents the coefficient of the high-order aspheric polynomial, x represents the function representation of the aspheric wavefront to be measured, and y and z represent the coordinate positions corresponding to the two-dimensional surface of the wavefront.

[0060] Furthermore, considering that the aspheric surface has rotational symmetry, the intersection line between the z=0 plane and the aspheric surface is selected to describe the aspheric surface shape function to be measured. Therefore, formula (1) can be re-expressed as:

[0061]

[0062] Furthermore, the aspheric surface to be measured is placed in a rectangular coordinate system. Figure 2 The spherical wave emitted from the source at point P returns to the aspherical surface to be measured with the wave path difference between the two, which is recorded as δ i For the i-th point on the initial reference sphere, the path difference between the point and the aspheric surface to be measured in the normal direction can be expressed by the following formula:

[0063]

[0064] Among them, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di The ordinate of a point D on the aspherical surface to be measured, y ci represents the ordinate of a point C on the initial reference surface, r 0 represents the radius of the initial reference surface, Represents the tangent distance between points C and D.

[0065] In practical applications, when δ i = ±jλ (j = 1, 2, 3...), the interference fringes generated by the optical path difference between the surface wave of the aspheric surface to be measured and the initial reference spherical wave are bright fringes. The distance between the centers of adjacent bright fringes is the fringe width, and its reciprocal is the interference fringe density. Based on this theoretical model, the density expression of the lateral shear interference fringes can be derived, where the position of the center point of the bright fringes can be determined by the following formula:

[0066]

[0067] Among them, T i represents the center point position of the i-th lateral shearing interference bright fringe, r 0 represents the radius of the initial reference surface, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di Indicates the ordinate of a point D on the aspherical surface to be measured, y ci The ordinate of a point C on the initial reference surface, R 0 represents the vertex curvature radius of the aspheric surface to be measured, k represents the cone coefficient of the quadratic surface, λ represents the wavelength, and S represents the shear amount.

[0068] In the above formula, S represents the shear amount, where the value of S is relative to the aspheric aperture. If the initial shear rate is defined, the shear amount can be determined by the following formula:

[0069] S=ratio 0 *D aspheric (5)

[0070] Among them, Ratio 0 represents the initial shear rate, D aspheric Indicates the aperture of the aspheric surface to be measured.

[0071] In the embodiment of the present invention, since the inverse of the position of the center point of the bright fringe is the interference fringe density, the interference fringe density can be expressed by the following formula:

[0072]

[0073] Where Density represents the fringe density of the lateral shearing interference pattern, T i represents the center point position of the i-th lateral shear interference bright fringe, T i-1 Indicates the center point position of the i-1th lateral shearing interference bright fringe.

[0074] In practical applications, since aspheric surface shape measurement is usually carried out using a reflective interferometer system, the optical path difference of the returned wavefront consists of the optical path difference from the reference spherical surface to the surface to be measured and the optical path difference from the surface to be measured to the reference spherical surface, and these two parts are equal in size. Therefore, the actual optical path difference of the returned wavefront should be twice the calculated optical path difference.

[0075] In a dual-grating lateral shearing interferometer with adjustable shear rate, the shear rate is generally controlled by the diffraction angle of the grating and the axial distance between the two gratings. The specific calculation formula is as follows:

[0076]

[0077] Where d represents the axial spacing between the grating and the reflector, ± represents the diffraction direction, λ represents the wavelength of light, Λ represents the diffraction polarization grating period, and D pupil Indicates the entrance pupil spot diameter.

[0078] In an embodiment of the present invention, based on the Nyquist fringe analysis principle and the influence of the actual interference pattern error, a rough optimization theoretical model of the shear rate can be jointly established, that is, a rough optimization shear rate selection theoretical model, which is as follows:

[0079]

[0080] Where D i (x di ,y di ) represents the aspheric wave equation to be measured, C i (x ci ,y ci) represents the initial reference spherical wave equation, RATIO represents the optimized shear rate, D aspheric represents the aperture of the aspheric surface to be measured, q is the number of available pixels of the detector, Ratio 0 represents the initial shear rate, Ratio 1 represents the rough optimized shear rate, Iteration range of initial shear rate, Density max represents the maximum resolvable threshold of the actual interference fringes, max[Density] represents the maximum lateral shearing interference pattern fringe density among the multiple lateral shearing interference pattern fringe densities, and the threshold is obtained according to the relationship curve between the interference pattern quality and the maximum resolvable threshold established by simulation.

[0081] Specifically, the radius theoretical model of the optimal reference surface is obtained by the following method:

[0082] In the embodiment of the present invention, the reverse optimization thinking is adopted to determine the radius of the optimal reference surface, and its principle can be summarized as follows: when the position corresponding to the radius of the initial reference surface is optimal, the mean value of the optical path difference returned by the aspheric surface to be measured is the smallest, and at this time, the range of aspheric surfaces that can be measured at the same shear rate is the largest. If the maximum range of shear rates can be selected, the position of the radius of the optimal reference surface corresponding to this time is the optimal value.

[0083] In order to reduce the time and space for iterative optimization of the radius of the optimal reference surface, the position of the vertex curvature radius of the aspheric surface to be measured is selected as the initial value of the iteration, and the intersection point R between the aperture edge normal and the x-axis of the aspheric surface to be measured is selected. n The position is taken as the maximum optimization range, as follows Figure 2 As shown. The theoretical model for determining the radius of the optimal reference surface by inverse optimization can be expressed as follows:

[0084]

[0085] Among them, Ratio max represents the first range of the rough optimized shear rate that matches the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(Ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rate, r 1 Indicates the radius of the best reference surface.

[0086] Specifically, the theoretical model for selecting the optimal shear rate is obtained by the following method:

[0087] In the embodiment of the present invention, the iterative process of fine-tuning the shear rate mainly considers the influence of the average fringe density and the interference pattern quality on the surface reconstruction accuracy. The average fringe density is specifically defined as the number of pixels on the target surface occupied by each fringe, which can be determined by the following formula:

[0088]

[0089] Among them, Density average represents the average fringe density of the lateral shearing interference pattern, M represents the number of bright fringes in the lateral shearing interference pattern, and T i Indicates the center point position of the lateral shearing interference bright fringes.

[0090] Specifically, Figure 3 The corresponding fringe patterns under different shear rates and the one-dimensional grayscale distribution along the shear direction are shown in Figure 3 It can be concluded that maintaining the average fringe density below 50 pixels / strip can ensure better shear differential wavefront reconstruction accuracy.

[0091] Based on this, an optimization theoretical model based on average stripe density is established, which can be specifically expressed as follows:

[0092]

[0093] Among them, Density average represents the average fringe density of the lateral shearing interferogram, M represents the number of bright fringes in the lateral shearing interference pattern, Ratio 2 Indicates the optimized shear rate, Ratio 1 represents the rough optimized shear rate, Represents the value range of the first range of the rough optimized shear rate.

[0094] In step 101, the basic parameters of the aspheric surface to be measured are determined as follows: the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, and the quadratic surface cone coefficient; the basic parameters of the aspheric surface to be measured are substituted into the aspheric surface wavefront function formula shown in formula (2). In practical applications, since it is a quadratic surface, the high-order coefficient A in formula (2) is 4 , A 6 , ..., A 2n are all zero, according to formula (2) we can get Figure 2 The aspheric curve equation in Figure 2 The radius of the initial reference surface can be set as the vertex curvature radius of the aspheric curve to be measured. Figure 2 Set the initial shear rate.

[0095] Further, according to Figure 2The horizontal coordinate and vertical coordinate of a certain point on the aspheric surface to be measured can be determined, and the horizontal coordinate and vertical coordinate of a certain point on the initial reference surface can also be determined; that is, the aspheric surface curve to be measured, the initial reference surface and the initial shear rate determined in step 101 are successively substituted into the above formulas (4), (5) and (6), and the shear amount, the center point position of the i-th transverse shear interference bright fringe and the transverse shear interference pattern fringe density can be obtained.

[0096] In step 102, the lateral shearing interference pattern fringe density Density obtained above, the detector target surface pixel size used for interference pattern acquisition, the maximum resolvable threshold of the actual interference fringe and the initial shear rate are substituted into formula (8), and the iteration optimization range of the initial shear rate given in formula (8) is sequentially iterated from 0.2 to 0, that is, the iteration is performed according to the iteration range of the initial shear rate and the second iteration step of the initial shear rate. If there is a maximum lateral shearing interference pattern fringe density among the multiple lateral shearing interference pattern fringe densities that is less than the maximum resolvable threshold of the actual interference fringe, the iteration can be stopped, and the roughly optimized shear rate is output according to the iteration result; if the above conditions are not met, it is necessary to continue the iteration and iterate according to the second iteration step.

[0097] Furthermore, the radius iteration range of the initial reference surface is set, and the first iteration step of the radius of the initial reference surface is determined. In the embodiment of the present invention, within each first iteration step, one round of iteration is performed according to the iteration range of the initial shear rate and the second iteration step to obtain a rough optimized shear rate; then, iteration is performed according to the first iteration step, and then a first iteration step is repeatedly performed to obtain a rough optimized shear rate; after executing multiple rounds of the first iteration step, according to formula (9), a maximum rough optimized shear rate is selected from multiple rough iterative optimized shear rates, and the radius of the initial reference surface corresponding to the maximum rough optimized shear rate is determined as the radius of the optimal reference surface, and then the first range of the rough optimized shear rate is determined according to the multiple rough iterative optimized shear rates, and the first range of the rough optimized shear rate matches the radius iteration range of the initial reference surface.

[0098] After the first range of the rough optimization shear rate and the radius of the optimal reference surface are determined, it can be determined that the rough optimization iteration is finished.

[0099] In step 103, the average fringe density of the lateral shearing interference pattern can be determined by formula (10) according to the number of bright fringes in the lateral shearing interference pattern and the center point position of the bright fringes in the lateral shearing interference pattern. Further, the radius of the best reference surface determined in the above step and the first range of the rough optimized shear rate are brought into formula (11), and the iteration is performed according to the first range of the rough optimized shear rate and the third iteration step of the rough optimized shear rate. At each third iteration step, if the average fringe density of the lateral shearing interference pattern is less than the judgment condition in formula (11), the fine optimized shear rate is obtained according to the average fringe density of the lateral shearing interference pattern. After multiple iterations according to the third iteration step within the first range of the rough optimized shear rate, multiple fine optimized shear rates can be obtained, and the first range of the fine optimized shear rate can be obtained according to the multiple fine optimized shear rates. If the condition is not met within the third iteration step, it is necessary to continue the iteration; in the embodiment of the present invention, the first range of the fine optimized shear rate matches the first range of the rough optimized shear rate, but the first range of the fine optimized shear rate is smaller than the first range of the rough optimized shear rate.

[0100] In order to more clearly introduce the method for selecting the lateral shear interference shear rate provided by the embodiment of the present invention, the following is combined with Figure 4 The method for selecting the lateral shear interference shear rate provided in an embodiment of the present invention is introduced in detail with specific numerical values.

[0101] like Figure 4 As shown, the method comprises the following steps:

[0102] Step 201: Select the basic parameters of the aspheric surface to be tested: the vertex curvature radius r of the aspheric surface to be tested 0 =348mm, quadratic conic coefficient k = -3.5, the aperture D of the aspheric surface to be measured aspheric =90mm, and the pixel size of the detector target surface used for interferogram acquisition is set to q=1024*1024pixels.

[0103] Step 202: Substitute the basic parameters of the aspheric surface to be tested in step 201 into the aspheric wavefront function shown in formula (2). Since the aspheric surface to be tested is a quadratic surface, the high-order coefficient A 4 , A 6 , ..., A 2n are all zero, according to formula (2) we can get Figure 2 The curve equation of the aspheric surface to be measured is shown in Figure 1. The radius of the initial reference surface is set to be the vertex curvature radius of the aspheric surface to be measured, r 0 =R 0 , set the initial shear rate to Ratio 0 =0.2.

[0104] Step 203: Substitute the aspheric curve equation to be measured, the initial reference surface curve equation and the initial shear rate obtained in step 202 into formula (4), formula (5) and formula (6) to obtain the shear amount, the center point position of the i-th lateral shear interference bright fringe and the lateral shear interference pattern fringe density.

[0105] Step 204: Substitute the lateral shearing interference pattern fringe density obtained in step 203 and the detector target surface pixel size q set in step 201 into formula (8), and iterate sequentially from 0.2 to 0 through the initial shear rate iterative optimization range given in formula (8). That is, iterate according to the iterative range of the initial shear rate and the second iterative step size of the initial shear rate.

[0106] Step 205: If there is a maximum lateral shearing interference pattern fringe density among multiple lateral shearing interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringes, the iteration can be stopped, and the coarse optimized shear rate is output according to the iteration result; if the above conditions are not met, it is necessary to continue to iterate in step 204 and iterate according to the second iteration step size.

[0107] Step 206: satisfying formula (8) to obtain a roughly optimized shear rate.

[0108] Step 207: Execute formula (9) and set the radius iteration range of the initial reference surface to r 0 ∈[R 0 , R n ]. And determine the first iteration step of the radius of the initial reference surface, and repeat steps 204, 205 and 206. If the condition of step 205 is met in each first iteration step, the coarse optimized shear rate selectable range corresponding to the radius of multiple optimal reference surfaces can be obtained.

[0109] Step 208, according to the judgment condition in formula (9), that is, whether the first range of rough optimized shear rates generated by multiple rough optimized shear rates includes the maximum rough optimized shear rate; if the condition is met, step 209 can be executed, if not, step 207 is repeated.

[0110] Step 209: Output the radius of the optimal reference surface as r 1 =357.08mm, the first range of the rough optimized shear rate is Ratio 1 ∈[0~0.035].

[0111] Step 210: Substitute the radius of the optimal reference surface determined in step 209 and the first range of the coarse optimized shear rate into formula (10) to calculate the average fringe density of the lateral shear interference pattern; further, substitute the radius of the optimal reference surface and the first range of the coarse optimized shear rate determined in the above steps into formula (11), and iterate according to the first range of the coarse optimized shear rate and the third iteration step of the coarse optimized shear rate, and iterate the first range of the coarse optimized shear rate from 0.035 to 0 in sequence.

[0112] Step 211: within the third iteration step, a fine optimized shear rate is obtained according to the average fringe density of the lateral shearing interference pattern. Within the first range of the coarse optimized shear rate, multiple iterations are performed according to the third iteration step. If the average fringe density of the lateral shearing interference pattern satisfies the judgment condition in formula (11), multiple fine optimized shear rates can be obtained. If the judgment condition is not met, execute step 210.

[0113] Step 212: According to a plurality of fine optimized shear rates, a first range of fine optimized shear rates can be obtained as Ratio∈[0.021~0.035].

[0114] That is, through the above steps, the basic parameters R of the aspheric surface to be measured are obtained. 0 =348mm, k=-3.5, D aspheric The first range of the fine optimization shear rate of the hyperbolic aspheric surface with a surface area of ​​90 mm is Ratio∈[0.021~0.030], and the fine optimization shear rate optimization is completed and the optimization results are output.

[0115] In summary, an embodiment of the present invention provides a method and device for selecting a shear rate by lateral shear interference, which comprehensively considers the influence of factors such as the surface parameters of the aspheric surface to be measured, the fringe density of the lateral shear interference pattern, the radius of the optimal reference surface and the actual interference pattern quality on the fringe analysis, and establishes a method for selecting a fine optimized shear rate through a coarse optimized shear rate selection theoretical model and a fine optimized shear rate selection theoretical model, wherein the coarse optimized shear rate selection theoretical model uses the fringe density of the lateral shear interference pattern and the radius of the initial reference surface as optimization targets to determine a first range of the coarse optimized shear rate, that is, a selectable range of the coarse optimized shear rate, and further uses the surface reconstruction accuracy as an optimization target to further select a fine optimized shear rate within the first range of the coarse optimized shear rate. The method provided by an embodiment of the present invention can solve the problem of unresolvable fringes and limited detection accuracy caused by random or theoretically unreferenced shear rate selection when using the lateral shear interference method for universal detection of multiple types of aspheric surfaces.

[0116] Based on the same inventive concept, an embodiment of the present invention provides a lateral shear interference shear rate selection device. Since the principle of solving the technical problem of the device is similar to that of a lateral shear interference shear rate selection method, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0117] like Figure 5 As shown, the device includes a first determining unit 301 , a first obtaining unit 302 , and a second obtaining unit 303 .

[0118] A first determining unit 301 determines the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function;

[0119] The first obtaining unit 302 determines the first iteration step of the radius of the initial reference surface according to the iteration range of the radius of the initial reference surface, and in each of the first iteration step, sequentially confirms the lateral shearing interference pattern fringe density corresponding to the initial shearing rate under the second iteration step according to the iteration range of the initial shearing rate and the second iteration step of the initial shearing rate, and obtains the rough optimized shearing rate and the first range of the rough optimized shearing rate matching the iteration range of the radius when there is a maximum lateral shearing interference pattern fringe density among the multiple lateral shearing interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringe when the rough optimized shearing rate and the first range of the rough optimized shearing rate matching the iteration range of the radius; and obtains the radius of the optimal reference surface according to the maximum rough optimized shearing rate included in the first range of the rough optimized shearing rate;

[0120] The second obtaining unit 303 determines the average fringe density of the lateral shearing interference pattern in turn according to the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate at each third iterative step according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface; when it is determined that the average fringe density of the lateral shearing interference pattern is less than the judgment condition, obtains the fine optimized shear rate and the first range of the fine optimized shear rate matching the first range of the coarse optimized shear rate according to the average fringe density of the lateral shearing interference pattern.

[0121] The first obtaining unit 302 is specifically used to obtain the rough optimized shear rate by the following formula:

[0122]

[0123] The rough optimized shear rate and the first range of the rough optimized shear rate matching the radius iteration range are obtained by the following formula:

[0124]

[0125] Wherein, Max[Density] represents the maximum lateral shearing interference pattern fringe density among the plurality of lateral shearing interference pattern fringe densities, and Density max Indicates the maximum resolvable threshold of the actual interference fringes, Ratio 1 represents the rough optimal shear rate, D aspheric represents the aperture of the aspheric surface to be measured, q represents the pixel size of the detector target surface, and y di represents the ordinate of a point D on the aspherical surface to be measured, represents the iteration range of the initial shear rate, λ represents the wavelength, Ratio max represents the first range of the rough optimized shear rate matching the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(Ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rate, r 1 Indicates the radius of the best reference surface.

[0126] The second obtaining unit 303 is specifically used for:

[0127] The judgment condition is that the average fringe density of the lateral shearing interference pattern is less than 50 pixels / strip;

[0128] The fine optimized shear rate and the first range of the fine optimized shear rate matching the first range of the coarse optimized shear rate are obtained by the following formula:

[0129]

[0130] Among them, Density average represents the average fringe density of the lateral shearing interferogram, M represents the number of bright fringes in the lateral shearing interference pattern, Ratio 2 Indicates the optimized shear rate, Ratio 1 represents the rough optimized shear rate, Represents the value range of the first range of the rough optimized shear rate.

[0131] Preferably, the first determining unit 302 is specifically configured to:

[0132] The shearing amount is determined by the following formula according to the aperture and initial shear rate of the aspheric surface to be tested:

[0133] S=Ratio 0 *D aspheric

[0134] According to the aspheric surface to be measured, the initial reference curved surface, the vertex curvature radius R of the aspheric surface to be measured 0And the shear amount is determined by the following formula to determine the center point position of the lateral shear interference bright fringe:

[0135]

[0136] The lateral shearing interference pattern fringe density matching the initial reference surface is determined by the following formula according to the center point positions of two adjacent lateral shearing interference bright fringes:

[0137]

[0138] Where S represents the shear amount, Ratio 0 represents the initial shear rate, D aspheric Indicates the aperture of the aspheric surface to be measured, T i represents the center position of the lateral shear interference bright fringe, r 0 represents the radius of the initial reference surface, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di Indicates the ordinate of a point D on the aspherical surface to be measured, y ci The ordinate of a point C on the initial reference surface, R 0 represents the vertex curvature radius of the aspheric surface to be measured, k represents the quadratic cone coefficient, λ represents the wavelength, and Density represents the fringe density of the lateral shearing interference pattern.

[0139] It should be understood that the units included in the above-mentioned lateral shear interference shear rate selection device are only logical divisions based on the functions implemented by the device. In practical applications, the above-mentioned units can be superimposed or split. And the functions implemented by the lateral shear interference shear rate selection device provided in this embodiment correspond one-to-one to the lateral shear interference shear rate selection method provided in the above-mentioned embodiment. The more detailed processing flow implemented by the device has been described in detail in the above-mentioned method embodiment 1 and will not be described in detail here.

[0140] Another embodiment of the present invention also provides a computer device, which includes: a processor and a memory; the memory is used to store computer program code, and the computer program code includes computer instructions; when the processor executes the computer instructions, the electronic device executes each step of the lateral shear interference shear rate selection method shown in the above method embodiment.

[0141] Another embodiment of the present invention further provides a computer-readable storage medium, which stores computer instructions. When the computer instructions are executed on a computer device, the computer device executes each step of the lateral shear interference shear rate selection method shown in the above method embodiment.

[0142] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0143] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A method for selecting a transverse shear interference shear rate, characterized in that: include: Determining the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function; According to the iteration range of the radius of the initial reference surface, the first iteration step of the radius of the initial reference surface is determined; within each of the first iteration step, according to the iteration range of the initial shear rate and the second iteration step of the initial shear rate, the lateral shear interference pattern fringe density corresponding to the initial shear rate under the second iteration step is confirmed in sequence; when there is a maximum lateral shear interference pattern fringe density among the multiple lateral shear interference pattern fringe densities that is less than the maximum analytical threshold of the actual interference fringe, a rough optimized shear rate and a first range of rough optimized shear rates matching the iteration range of the radius are obtained; according to the maximum rough optimized shear rate included in the first range of rough optimized shear rates, the radius of the optimal reference surface is obtained; According to the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate, at each third iterative step, the average fringe density of the lateral shear interference pattern is determined in sequence according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the lateral shear interference pattern is less than the judgment condition, the fine optimized shear rate and the first range of the fine optimized shear rate matching the first range of the coarse optimized shear rate are obtained according to the average fringe density of the lateral shear interference pattern.

2. The method according to claim 1, characterized in that When there is a maximum lateral shearing interference pattern fringe density that is less than the maximum analytical threshold of the actual interference fringe, the rough optimized shear rate is obtained by the following formula: Wherein, Max[Density] represents the maximum lateral shearing interference pattern fringe density among the plurality of lateral shearing interference pattern fringe densities, and Density max represents the maximum resolvable threshold of the actual interference fringes, Ratio1 represents the rough optimized shear rate, and D aspheric represents the aperture of the aspheric surface to be measured, q represents the pixel size of the detector target surface, and y di represents the ordinate of a point D on the aspherical surface to be measured, represents the iteration range of the initial shear rate and λ represents the wavelength.

3. The method according to claim 1, characterized in that The rough optimized shear rate and the first range of the rough optimized shear rate matching the radius iteration range are obtained by the following formula: Among them, Ratio max represents the first range of the rough optimized shear rate matching the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(Ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rates, and r1 represents the radius of the optimal reference surface.

4. The method according to claim 1, characterized in that The judgment condition is that the average fringe density of the lateral shearing interference pattern is less than 50 pixels / strip; When it is determined that the average fringe density of the lateral shearing interference pattern is less than the judgment condition, the fine optimized shearing rate and the first range of the fine optimized shearing rate matching the first range of the coarse optimized shearing rate are obtained by the following formula: Among them, Density average represents the average fringe density of the lateral shearing interferogram, M represents the number of bright fringes in the lateral shearing interference pattern, Ratio2 represents the fine optimized shearing rate, Ratio1 represents the coarse optimized shearing rate, Represents the value range of the first range of the rough optimized shear rate.

5. The method according to claim 1, characterized in that The step of sequentially determining the fringe density of the transverse shear interference pattern corresponding to the initial shear rate under the second iteration step specifically includes: The shearing amount is determined by the following formula according to the aperture and initial shear rate of the aspheric surface to be tested: S=Ratio0*D aspheric The center point position of the lateral shear interference bright fringe is determined by the following formula according to the aspheric surface to be measured, the initial reference curved surface, the vertex curvature radius R0 of the aspheric surface to be measured and the shear amount: The lateral shearing interference pattern fringe density matching the initial reference surface is determined by the following formula according to the center point positions of two adjacent lateral shearing interference bright fringes: Where S represents the shear amount, Ratio0 represents the initial shear rate, and D aspheric Indicates the aperture of the aspheric surface to be measured, T i represents the center point of the lateral shear interference bright fringe, r0 represents the radius of the initial reference surface, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di Indicates the ordinate of a point D on the aspherical surface to be measured, y ci represents the ordinate of a point C on the initial reference surface, R0 represents the vertex curvature radius of the aspheric surface to be measured, k represents the cone coefficient of the quadratic surface, λ represents the wavelength, and Density represents the fringe density of the lateral shearing interference pattern.

6. The method according to claim 1, characterized in that After determining the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface, the method further includes: The aspheric surface to be measured is placed in a rectangular coordinate system, and the path difference between the initial reference surface and the aspheric surface to be measured is determined. The path difference is as follows: Among them, x di Indicates the horizontal coordinate of the point D on the aspheric surface to be measured, x ci represents the horizontal coordinate of a point C on the initial reference surface, y di The ordinate of a point D on the aspherical surface to be measured, y ci represents the ordinate of a point C on the initial reference surface, r0 represents the radius of the initial reference surface, Represents the tangent distance between points C and D.

7. A lateral shear interference shear rate selection device, characterized in that: include: A determination unit, configured to determine the vertex curvature radius of the aspheric surface to be measured as the radius of the initial reference curved surface according to the aperture of the aspheric surface to be measured, the vertex curvature radius of the aspheric surface to be measured, the quadratic surface cone coefficient and the aspheric surface wavefront function; A first obtaining unit is used to determine a first iteration step of the radius of the initial reference surface according to an iteration range of the radius of the initial reference surface, and within each of the first iteration step, sequentially confirm the lateral shearing interference pattern fringe density corresponding to the initial shearing rate under the second iteration step according to the iteration range of the initial shearing rate and the second iteration step of the initial shearing rate, and when there is a maximum lateral shearing interference pattern fringe density among a plurality of the lateral shearing interference pattern fringe densities that is less than a maximum analytical threshold of the actual interference fringe, obtain a rough optimized shear rate and a first range of rough optimized shear rates that matches the iteration range of the radius; and obtain the radius of the optimal reference surface according to the maximum rough optimized shear rate included in the first range of rough optimized shear rates; The second obtaining unit is used to determine the average fringe density of the lateral shearing interference pattern in turn according to the first range of the coarse optimized shear rate and the third iterative step of the coarse optimized shear rate at each third iterative step according to the first range of the coarse optimized shear rate and the radius of the optimal reference surface. When it is determined that the average fringe density of the lateral shearing interference pattern is less than the judgment condition, the fine optimized shear rate and the first range of fine optimized shear rate matching the first range of the coarse optimized shear rate are obtained according to the average fringe density of the lateral shearing interference pattern.

8. The device according to claim 7, characterized in that The first obtaining unit is specifically used to obtain the rough optimized shear rate by the following formula: The rough optimized shear rate and the first range of the rough optimized shear rate matching the radius iteration range are obtained by the following formula: Wherein, Max[Density] represents the maximum lateral shearing interference pattern fringe density among the plurality of lateral shearing interference pattern fringe densities, and Density max represents the maximum resolvable threshold of the actual interference fringes, Ratio1 represents the rough optimized shear rate, and D aspheric represents the aperture of the aspheric surface to be measured, q represents the pixel size of the detector target surface, and y di represents the ordinate of a point D on the aspherical surface to be measured, represents the iteration range of the initial shear rate, λ represents the wavelength, Ratio max represents the first range of the rough optimized shear rate matching the radius iteration range, Indicates the iteration range of the radius of the initial reference surface, Max(Ratio max ) represents the maximum rough optimized shear rate included in the first range of rough optimized shear rates, and r1 represents the radius of the optimal reference surface.

9. A computer device, characterized in that: The computer device includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the lateral shear interference shear rate selection method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that: A computer program is stored, and when the computer program is executed by a processor, the processor executes the lateral shear interference shear rate selection method as described in any one of claims 1-7.

Images