System for inspecting surfaces of an optical wave using a gradient density filter

Description

[0001] The technical field of the invention is that of the measurement and control of optical wave surfaces. A large number of technical fields require the control of wave surfaces. More particularly, but not exhaustively, mention will be made of the quality control of optical surfaces or optical systems, the control of adaptive optics used in fields ranging from astronomy to ophthalmology.

[0002] Optical surface quality control is an extremely broad field that includes the metrology of individual optical components, the alignment of complex optical systems, or the evaluation of laser beam quality. It covers the visible, infrared, and ultraviolet spectral ranges. The measuring devices currently used are interferometers, which require the development of larger systems, or more compact wavefront sensors with lower accuracy and resolution. Additional information on this topic can be found in D. Malacara's book "Optical Shop Testing," Third Edition, Willey 2007.

[0003] Large telescopes used for astronomy include adaptive optics systems that require wavefront sensors. These systems are not necessarily well-suited to observing extended objects such as galaxies or globular clusters. Furthermore, these systems may include artificial stars obtained from laser beams. In this case, adaptive optics systems are necessarily complex since they include as many wavefront sensors as artificial stars. Further information on this topic can be found in the following publications: JW Hardy, JE Lefebvre, CL Koliopoulos titled “Real-time atmospheric compensation” J. Opt. Soc. Am. Vol. 67, p. 360-369 (1977), RV Shack, BC Platt entitled “Production and use of a lenticular Hartmann screen” J. Opt. Soc. Am. Vol. 61, p. 656 (1971), J. Primot, N. Guérineau entitled “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard”, published in Applied Optics vol. 39, pp. 5715-5720 (2000).

[0004] In ophthalmology, adaptive optics systems based on the use of point laser sources are also used, which can pose other operational problems. Further information on this topic can be found in the publication by J. Lang, B. Grimm, S. Goelz, J.F. Bille, entitled "Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wavefront sensor", published in J. Opt. Soc. Am. A, vol. 11, pp. 1949-2685 (1994).

[0005] An optical wavefront control system that does not have the above drawbacks is disclosed in Hénault et al.: "Crossed-sine wavefront sensor for adaptive optics, metrology and ophthalmology applications", ENGINEERING RESEARCH EXPRESS, vol. 2, 015042, March 4, 2020, pages 1-14. It comprises an optical head that only includes optical elements that are simple to produce and image processing. More specifically, the optical device comprising an exit pupil, said control system comprising an optical measuring head and a computer for processing images from said optical measuring head, in which the optical measuring head comprises: ∘ a density gradient filter, in a plane referenced (x', y') perpendicular to the optical axis of the optical measuring head, the transmission T(x', y') of said filter being governed by the equation: T x ′ , y ′ = 1 + sin 2 π x ′ − y ′ / p x sin 2 π x ′ + y ′ / p y 2 px and py representing the periods of the two sinusoidal functions depending respectively on (x'-y') and (x'+y'). ∘ a matrix frame of identical lenses, square in shape, with the same focal length, said matrix frame comprising at least four lenses, each center of one of the four lenses being arranged on an axis passing through the center of the exit pupil and a point O'M'(i, j) of the density gradient filter such that, in the plane referenced (x', y'), O ′ M i , j ′ = i m + 0.25 p x / 2 j n + 0.25 p y / 2 i and j being able to take the values ​​-1 and +1, m and n being positive or zero integers. ∘ a matrix of photodetectors, each of the four lenses forming an image of the pupil in the plane of this matrix, these images being referenced I" k (x, y), k varying from 1 to 4; the image processing computer includes calculation means for calculating the partial derivatives ∂ Δ ∂ x x y And ∂ Δ ∂ y x y of the wave surface Δ(x, y) in the plane of the exit pupil, these partial derivatives being equal to ∂ Δ ∂ x x y = Ax + B sin − 1 I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y C ∂ Δ ∂ y x y = Ay + B sin − 1 I 4 " x y + I 3 " x y − I 2 " x y − I 1 " x y C A, B and C being constants depending on the geometric parameters of the optical measuring head.

[0006] The invention relates to a system for controlling an optical wave surface from an optical device, said optical device comprising an exit pupil, said control system comprising an optical measuring head and a computer for processing images from said optical measuring head, in which - - the optical measuring head comprises: ∘ a density gradient filter, in a plane referenced (x', y') perpendicular to the optical axis of the optical measuring head, the transmission T(x', y') of said filter being governed by the equation: T ij x ′ , y ′ = 1 + 2 π idx ′ / p x − jdy ′ / p x 2 with dx ′ dy ′ = x ′ − i m + 0.25 p x / 2 y ′ − j n + 0.25 p y / 2 px and py representing the periods associated with two sinusoidal functions depending respectively on dx' and dy', i and j being able to take the values ​​-1 and +1, m and n being positive or zero integers, ∘ a matrix frame of identical lenses, square in shape, with the same focal length, said matrix frame comprising at least four lenses, each center of one of the four lenses being arranged on an axis passing through the center of the exit pupil and a point O'M'(i, j) of the density gradient filter such that, in the plane referenced (x', y'), O ′ M i , j ′ = i m + 0.25 p x / 2 j n + 0.25 p y / 2 ∘ a matrix of photodetectors, each of the four lenses forming an image of the pupil in the plane of this matrix, these images being referenced I" k (x, y), k varying from 1 to 4; - - the image processing computer includes calculation means for calculating the partial derivatives ∂ Δ ∂ x x y And ∂ Δ ∂ y x y of the wave surface Δ(x, y) in the plane (x, y) of the exit pupil, these partial derivatives being equal to ∂ Δ ∂ x x y = Ax + B I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y ∂ Δ ∂ y x y = Ay + B I 4 " x y + I 3 " x y − I 2 " x y − I 1 " x y

[0007] A and B being constants depending on the geometric parameters of the optical measuring head.

[0008] The invention will be better understood and other advantages will appear on reading the description which follows, given without limitation and thanks to the appended figures among which: There figure 1 represents a general view of the control system according to the invention; The figure 2 represents the optical measuring head of a control system applicable to the invention; The figure 3 represents the maxima and minima of the cross-sine density gradient filter used in the article by Hénault et al; The figure 4 represents the level curves of the central part of the cross-sine filter; The figure 5 represents a first distribution of the lenses of the matrix frame applicable to the invention; The figure 6 represents a second distribution of the lenses of the matrix frame applicable to the invention; The figure 7 represents a third distribution of the lenses of the matrix frame applicable to the invention; The figure 8 represents a fourth distribution of the lenses of the matrix frame applicable to the invention; The figure 9 represents a transmission map of the cross-sine filter; and The figure 10 represents a transmission map of the filter according to an embodiment of the invention.

[0009] The general block diagram of the optical wave surface control system according to the invention is shown in the figure 1 . It essentially comprises an optical head 10 and an image processing computer 20. The optical head comprises a matrix of photodetectors 13. This is connected to a first display device 21 which displays the images from the matrix of photodetectors. In the same way, the image processing computer comprises a second display device 22 making it possible to display, among other things, the processed images and the information necessary for processing.

[0010] This system is intended to control an optical device 1. This forms a light image from a luminous object 2 or a light source. When the optical device is a lens, this image is real. When the device is an afocal system, the image is at infinity. As will be seen in the remainder of the description, the control system according to the invention is capable of controlling these two types of optical devices. In the case of figure 1 , the optical device is a lens.

[0011] The optical device 1 comprises a pupil 3. The purpose of the control system is to measure the wave surface of the light image given by the optical device at the level of this pupil. The pupil is generally circular in shape. It may comprise a central obturation and its possible support.

[0012] The optical head according to the invention is shown in figure 2 It essentially comprises a density gradient filter 11, a matrix frame of lenses 12 and the matrix 13 of photodetectors as previously indicated.

[0013] In order to determine the respective positions of these different elements, the following conventions have been adopted.

[0014] We denote OXYZ the reference frame attached to the pupil of the optical device. The point O corresponds to the center of the pupil and OZ is the optical axis of the optical device. The X axis is perpendicular to the plane of the figure 2 . The points P of the pupil located in the OXY plane are designated by their Cartesian coordinates (x, y). In this frame, the wave surface to be measured is noted Δ(x, y).

[0015] We note f the distance which separates the plane of the pupil from the plane of focus of the optical device and F the point of intersection of this plane of focus with the optical axis.

[0016] We denote by O'X'Y'Z the reference frame attached to the plane of the density gradient filter. The X' axis is perpendicular to the plane of the figure 2 . Point O' is located on the optical axis at a distance z' equal to FO' from the focusing plane. The points M of the filter located in the plane O'X'Y' are designated by their Cartesian coordinates (x', y').

[0017] We note FX 1 Y 1 Z the reference frame attached to the focal plane of the optical device. The X 1 axis is perpendicular to the plane of the figure 2 . The points I located in the plane FX 1 Y 1 are designated by their Cartesian coordinates (x 1 , y 1 ). The lens matrix frame is located in this plane.

[0018] Finally, we note O"X"Y"Z the reference frame attached to the matrix of photodetectors. The X" axis is perpendicular to the plane of the figure 2 . The pupil images formed by the lenses of the matrix frame are located in the O"X"Y" plane. The point O" is located on the optical axis at a distance z" from the FX 1 Y 1 plane. The points P" located in this O"X"Y" plane are designated by their Cartesian coordinates (x", y").

[0019] The gradient density filter is located in the O'X'Y' plane. The transmission of the filter used in the article by Hénault and AI. T(x', y') is equal to the product of two sinusoidal functions rotated 45 degrees around the optical axis. More precisely, the transmission of the filter is equal to: T x ′ , y ′ = 1 + sin 2 π x ′ − y ′ / p x sin 2 π x ′ + y ′ / p y 2 px and py represent the spatial periods of the two sinusoidal functions. These periods can be different. In the following description, we consider that these periods are identical and equal to p.

[0020] The minima of the function T(x', y') are equal to 0 and the maxima are equal to 1. The figure 3 represents the distribution of these minima and maxima in the O'X'Y' plane of the density gradient filter in the case of identical periods on both axes. On this figure 3 , maxima are represented by white circles and minima by black circles.

[0021] There figure 4 represents the transmission curves of the same value in the O'X'Y' plane limited on both axes to values ​​between -p / 4√2 and +p / 4√2. The thickest lines correspond to the lowest transmission values.

[0022] The filter may also include an opaque mask with circular openings. The location of each opening corresponds to that of a lens in the matrix frame and its diameter is adapted to the dimensions of this lens. More generally, the shape of the mask corresponds to that of the pupil of the lens.

[0023] This filter can be manufactured using various technologies, including optical or electronic lithography, nano-imprinting, holographic plate recording or liquid crystal modulators.

[0024] The matrix frame of mini-lenses 12 is located in the plane FX 1 Y 1 . All the lenses that compose it are identical and of square section. The dimensions of the lenses are between a few millimeters and a few centimeters. The tolerances on the design and manufacture of these lenses must be such that they do not disturb the wave surface to be analyzed. This does not present any particular difficulties for the person skilled in the art, given the small aperture of these lenses.

[0025] The focal length f L of the mini-lenses is adjusted so that each of them forms an image of the pupil in the O"X"Y" plane of the photodetector array.

[0026] This frame has 4k lenses, k being an integer greater than or equal to 1. The frame can therefore have four lenses, eight lenses, twelve lenses and so on. The lenses are organized in groups of four arranged symmetrically around the optical axis. Each center of one of the four lenses in the group is arranged on an axis passing through the center O of the exit pupil and a point O'M'(i, j) of the density gradient filter such that, in the plane referenced (x', y'), O ′ M i , j ′ = i m + 0.25 p x / 2 j n + 0.25 p y / 2 i and j can take the values ​​-1 and +1, m and n being positive or zero integers.

[0027] The coordinates of the four centers I i,j of the lenses of each group in the plane FX 1 Y 1 are deduced from the relation: OI i , j = f f + z ′ OM i , j ′

[0028] THE figures 5, 6 , 7 et 8 illustrate four examples of possible distributions of said lenses 12. They are represented in the plane FX 1 Y 1 . In these figures, the period p is the same on both axes. These figures also include the density gradient filter.

[0029] On the figure 5 , the frame has a single group of four lenses. In this example, the integers m and n are zero and we have: O ′ M i , j ′ = 0.25 ip / 2 0.25 jp / 2

[0030] This configuration is the simplest to achieve since it includes a minimum of lenses and, moreover, they are glued to each other.

[0031] On the figure 6 , the frame also has a single group of four lenses. In this example, m and ne are equal to 1 and we have: O ′ M i , j ′ = 1.25 ip / 2 1.25 jp / 2

[0032] On the figure 7 , the frame includes the two groups of four lenses of the figures 5 et 6 .

[0033] On the figure 8 , the frame has two groups of four lenses. The centers of the first and second groups verify: O ′ M i , j ′ = 0.25 ip / 2 1.25 jp / 2 et O ′ M i , j ′ = 1.25 ip / 2 0.25 jp / 2

[0034] The photodetector matrix is ​​arranged in the O"X"Y" plane in which the pupil images formed by the lenses of the matrix frame are located. The sensitivity of the photodetector matrix is ​​adapted to the spectral band of the luminous object or the light source to be controlled. This matrix has a number of detectors adapted to the desired spatial resolution. For example, a matrix of 2048x2048 pixels is sufficient to achieve a maximum spatial resolution of 1000x1000 on the wave surface.

[0035] In the above, the optical device is an objective, its focal plane is located in the plane of the matrix frame of the lenses. When the optical device is an afocal, the optical measuring head comprises an additional optic arranged in the exit pupil, so that the focal plane of said additional optic is located in the plane of the matrix frame of the lenses.

[0036] It is also possible, regardless of the type of optical device to be measured, to add a variable focal length optic to optimize control by zooming, for example, on a particular area of ​​the pupil.

[0037] The image processing computer performs the following functions. Its first function is to store the raw images received by the photodetector array. Its second function is to calibrate these raw images in order to correct the uniformity errors of the pixels in the photodetector array. This calibration is obtained from known images recorded during a prior calibration phase.

[0038] The image thus calibrated is separated into as many secondary images as there are lenses in the matrix frame. Each secondary image is the image of the pupil of the optical device given by a particular lens. These secondary images are recentered in the plane of the pupil. Each of the images has an intensity distribution noted I k " x y , k being the index of the secondary image.

[0039] The analytical expressions for the intensity distributions of the images are obtained from Fresnel diffraction analysis. Information on this method can be found in the publication by F. Hénault, “Fresnel diffraction analysis of Ronchi and reverse Hartmann tests”, submitted to J. Opt. Soc. Am. A.

[0040] As an example, for a four-lens configuration as shown in the figure 5 , these distributions are as follows: I 1 " x y = 5 16 − cos γ 4 sin φ X ′ / 2 + cos γ 4 sin φ Y ′ / 2 − 1 8 sin φ X ′ / 2 sin φ Y ′ / 2 − 1 32 cos 2 φ X ′ − 1 32 cos 2 φ Y ′ I 2 " x y = 5 16 + cos γ 4 sin φ X ′ / 2 + cos γ 4 sin φ Y ′ / 2 + 1 8 sin φ X ′ / 2 sin φ Y ′ / 2 − 1 32 cos 2 φ X ′ − 1 32 cos 2 φ Y ′ I 3 " x y = 5 16 − cos γ 4 sin φ X ′ / 2 − cos γ 4 sin φ Y ′ / 2 + 1 8 sin φ X ′ / 2 sin φ Y ′ / 2 − 1 32 cos 2 φ X ′ − 1 32 cos 2 φ Y ′ I 4 " x y = 5 16 + cos γ 4 sin φ X ′ / 2 − cos γ 4 sin φ Y ′ / 2 − 1 8 sin φ X ′ / 2 sin φ Y ′ / 2 − 1 32 cos 2 φ X ′ − 1 32 cos 2 φ Y ′

[0041] We have, using the previous notations: φ x ′ = 2 π f + z ′ p ∂ Δ ∂ x x y + 2 πz ′ fp x , φ y ′ = 2 π f + z ′ p ∂ Δ ∂ y x y + 2 πz ′ fp y And γ = 4 πλ z ′ f + z ′ fp 2 ∂ Δ ∂ x x y And ∂ Δ ∂ y x y represent the derivatives of the wave surface at each point P of the pupil.

[0042] The dimensionless parameter y typically takes a very small value (generally of the order of 10 -4< ).

[0043] From the secondary images, it is then possible to calculate these two derivatives of the wave surface. We obtain: ∂ Δ ∂ x x y = z ′ f f + z ′ x + p 2 π 2 f + z ′ sin − 1 I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y cos γ And ∂ Δ ∂ y x y = z ′ f f + z ′ y + p 2 π 2 f + z ′ sin − 1 I 4 " x y + I 3 " x y − I 2 " x y − I 1 " x y cos γ

[0044] Finally, it is possible to reconstruct the wavefront Δ(x, y) from these two partial derivatives by integrating them. Further information on this point can be found in the publication by F. Roddier, C. Roddier, “Wavefront reconstruction using iterative Fourier transforms,” Applied Optics vol. 30, p 1325-1327 (1991).

[0045] The optimization of the spatial period of the density gradient filter must satisfy two opposing constraints.

[0046] The equations giving the phase variations φ'x and φ'y show that the quantities to be measured ∂ Δ ∂ x x y And ∂ Δ ∂ y x y are amplified by a factor g which we call gain and which is worth: g = 2 π 2 f + z ′ / p .

[0047] Choosing a high gain maximizes intensity variations in the acquired images. Respecting this sensitivity criterion favors short spatial periods in order to minimize the parameter p.

[0048] Furthermore, the use of a filter constructed from periodic functions results in a replication effect of the image of the pupil of the optical device to be measured. This effect results in the relative decentering ρ of the secondary images. We demonstrate that this parameter is: ρ = λ f + z ′ Dp , D being the diameter of the pupil.

[0049] This parameter should be as low as possible, typically less than 1%, which leads to favoring long spatial periods.

[0050] It is possible to establish a compromise between these two antagonistic tendencies by means of a least squares criterion C which is: C = ρ 2 + w 2 g 2 = λ 2 f + z ′ 2 D 2 p 2 + w 2 p 2 4 π 2 f + z ′ 2

[0051] Where w is a scale factor between 10 3< and 10 4< . The minimum of the criterion is reached when the period p 0 is: p 0 = f + z ′ 2 πλ wD

[0052] This period p 0 can be refined by means of simulations.

[0053] For example, for a telescope with a focal length of 100 meters, an aperture of 10 meters and used in the visible at a wavelength centered on 0.5 microns, the optical head being placed at the focus of this telescope, the spatial period of the filter is 1 millimeter.

[0054] The measurement accuracy achieved is of the order of a hundredth of a wavelength and the measurement time is less than a hundredth of a second. This time is short enough to overcome disturbances generated by the environment such as micro-vibrations and atmospheric turbulence.

[0055] According to the invention, the density gradient filter has an optical transmission T(x', y') which varies in a piecewise linear manner, governed by the equation T ij x ′ , y ′ = 1 + 2 π i dx ′ / p x − j dy ′ / p x 2 with d x ′ d y ′ = x ′ − i m + 0.25 p x / 2 y ′ − j n + 0.25 p y / 2

[0056] Equation (26), (27) is obtained by limited development to the first order of the sine functions of equation (1) in the vicinity of the points M' ij defined by (2).

[0057] THE figures 9 et 10 show, respectively, the transmission map of a filter defined by equation (1) - called "cross-sine" and by equations (26), (27) - called "linear" - in the case where px =py =p.

[0058] The main advantage of the embodiment according to the invention is that the calculations necessary to obtain the partial derivatives from the images from said optical measuring head are simpler than in the case of the crossed sine filter. It is in fact possible to demonstrate that we then have: ∂ Δ ∂ x x y = Ax + B I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y ∂ Δ ∂ x x y = Ay + B I 4 " x y + I 3 " x y − I 2 " x y − I 1 " x y A and B being constants depending on the geometric parameters of the optical measuring head.

[0059] For a four-lens configuration as shown in the figure 5 , but with a filter defined by equations (26), (27) we have in particular: ∂ Δ ∂ x x y = z ′ f f + z ′ x − p 4 2 f + z ′ I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y ∂ Δ ∂ y x y = z ′ f f + z ′ y − p 4 2 f + z ′ I 4 " x y + I 3 " x y − I 2 " x y − I 1 " x y Where f and z' were defined with reference to the cross-sine filter.

[0060] Numerical simulations carried out with the same calculation codes as in the case of the "cross-sine" filter of equation (1) have shown that the optical wave surface control system equipped with the "linear" filter of equations (26) and (27) makes it possible to achieve equivalent measurement accuracies.

Claims

1. System for inspecting an optical wave surface from an optical device (1), the optical device comprising an exit pupil (3), the monitoring system comprising an optical measuring head (10) and a computer (20) for processing images from the optical measuring head, wherein - the optical measuring head comprises: ∘ a gradient density filter (11), in a plane referenced (x', y') perpendicular to the optical axis of the optical measuring head, the transmission T(x', y') of the filter being governed by the equation: T ij x ′ , y ′ = 1 + 2 π idx ′ / p x − jdy ′ / p x 2 where dx ′ dy ′ = x ′ − i m + 0.25 p x / 2 y ′ − j n + 0.25 p y / 2 px and py representing the periods associated with two sinusoidal functions dependent respectively on dx' and dy'), i and j being able to take the values -1 and +1, and m and n being positive integers or nil, ∘ a matrix array of identical, square-shaped lenses (12) of the same focal length, the matrix array comprising at least four lenses, each center of one of the four lenses being arranged on an axis passing through the center of the exit pupil and a point O'M'(i, j) of the gradient density filter such that, in the plane referenced (x', y'), O ′ M i , j ′ = i m + 0.25 p x / 2 j n + 0.25 p y / 2 ∘ an array (13) of photodetectors, each of the four lenses forming an image of the pupil in the plane of this array, these images being referenced I"k(x, y), k varying from 1 to 4; - the computer (20) for processing the images comprises calculation means for calculating the partial derivatives ∂ Δ ∂ x x y and ∂ Δ ∂ y x y of the wave surface Δ(x, y) in the plane (x, y) of the exit pupil, these partial derivatives being equal to ∂ Δ ∂ y x y = Ax + B I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y ∂ Δ ∂ y x y = Ay + B I 4 " x y − I 3 " x y + I 2 " x y − I 1 " x y A and B being constants dependent on the geometric parameters of the optical measuring head.

2. Inspection system according to claim 1 wherein, when the optical device is a lens, its focusing plane is located in the plane of the matrix array of the lenses.

3. Inspection system according to claim 1 wherein, when the optical device is an afocal, the optical measuring head comprises an additional optic arranged in the exit pupil, such that the focusing plane of said additional optic is located in the plane of the matrix array of the lenses.

4. Inspection system according to any of the preceding claims, wherein the matrix array comprises at least one second quadruplet of lenses.

5. Inspection system according to any of the preceding claims, wherein the two periods px and py are equal.