JPH06235619A - Measuring device for wavefront aberration - Google Patents

Abstract

PURPOSE:To instantaneously measure a wavefront by converting interference fringes to coordinates by a coordinate converting hologram element and inputting an image input signal to a neural network which has finished learning with the use of known data of the kind and the amount of aberrations. CONSTITUTION:An interferometer 1 obtains a wave surface 2 including interference fringes generated by a wave surface of a to-be-detected object and a reference wave surface. The interference fringes are converted to polar coordinates by a coordinate converting hologram 3 and detected by a CCD camera 4. The data taken into the camera 4 is divided into pixels of a predetermined size on a computer 5. Each pixel is input to a neuron of an input layer of a neural network constructed by software on the computer 5.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a wavefront aberration measuring device for determining the type and amount of aberration from interference fringes generated by a reference wavefront and an object wavefront from an object to be measured when measuring a spherical shape or the like. .

[0002]

2. Description of the Related Art In processing a lens or inspecting a processed lens, an object to be inspected is set in an interferometer, and fringe analysis of interference fringes generated from the object to be inspected is performed to determine the amount and type of aberration. Is often performed to determine the reprocessed portion of the lens and to determine the quality. As a method for the fringe analysis, a method using Zernike coefficients is generally used. The wavefront aberration W (ρ, θ) is calculated by Zernike polynomial R _i (ρ, θ)
When expressed by, it becomes the following formula.

[0003] Z _{i in} equation (1) is the Zernike coefficient. The Zernike coefficient indicates the amount of aberration according to the Zernike polynomial R _i corresponding to each type of aberration, some of which are shown in Table 1 below.

[0004] Such a Zernike polynomial is a combination of aberrations that are orthogonal within a unit circle having a radius of 1, the value on the circumference of the unit circle is 1, and the RMS (mean square) value of the corresponding aberration is minimized. It has features such as
This is a very excellent method that can obtain the aberration coefficient of a desired aberration without being affected by other orders and other aberrations.

[0005]

However, in the above-mentioned method using the Zernike polynomial of the conventional example, the aberration coefficient of the desired aberration is actually calculated by a computer in the following complicated procedure. ing.

First, in order to reduce the amount of calculation from the obtained interference fringes and improve the processing speed, a plurality of points are sampled. For sampling, it is not possible to directly obtain Zernike coefficients from a Zernike polynomial as an orthogonal function due to errors and continuity problems. The converted coefficient is further converted to Zernike coefficient using the conversion matrisk,
It takes a considerable amount of processing time. In particular, the processing time is fatal for a processed product inspection or the like that needs to inspect a large amount of inspection objects.

The present invention has been made in order to solve the above-mentioned conventional problems, and its purpose is to identify the type and amount of aberration from the interference fringes generated by the reference wavefront and the object wavefront from the object to be measured. The object is to provide a wavefront aberration measuring device capable of instantaneously outputting.

[0008]

Means for Solving the Problems A wavefront aberration measuring instrument of the present invention that achieves the above object is a hologram element for performing coordinate conversion on interference fringes generated by a reference wavefront and an object wavefront from an object to be inspected, and , The image converted by the hologram element is used as an input signal, the excitation layer of a neuron group in the input layer, which is composed of a plurality of neuron groups receiving the signal, and the excitation pattern of the neuron group in the preceding layer are received, and the pattern conversion is performed. 1 consisting of a group of neurons that output excitation patterns to the stage
The neural network has a layer or a plurality of intermediate layers and an output layer that receives and converts the excitation pattern of the final neurons of the intermediate layer and outputs the output.

In this case, the neural network inputs a plurality of pieces of interference fringe information whose types and amounts of aberrations are known, and determines the size of the coupling of neurons between each layer by error backpropagation learning.

[0010]

In the present invention, with the above-mentioned structure,
The coordinate conversion of the information of the interference fringes generated by the reference wavefront and the object wavefront, which is necessary when expanding to the Zernike polynomial, can be instantaneously processed by using the hologram element.

Further, the above-mentioned neural network completes learning in advance by using interference fringes having typical aberrations whose coefficients of the corresponding Zernike polynomials are known. Since the calculation method to obtain is already determined as the magnitude of the coupling between neurons, and the magnitude of the coupling also expresses the orthogonality of the Zernike coefficients, the general interference fringes for which the type and amount of aberration are to be measured. By inputting, the Zernike coefficient can be obtained instantaneously and accurately.

From the above, it can be seen that the wavefront aberration measuring device of the present invention can significantly reduce the processing time as compared with the conventional method using a computer.

[0013]

Embodiments of the wavefront aberration measuring device of the present invention will be described below with reference to the drawings. FIG. 1 is a diagram showing a schematic configuration of a wavefront aberration measuring device according to one embodiment. In the figure, reference numeral 1 denotes an object to be inspected arranged in a system and an object wavefront and a reference wavefront by the object to be inspected. This is an interferometer for obtaining the wavefront 2 including the generated interference fringes. In the case of this embodiment, a Fizeau interferometer is used. Reference numeral 3 is a kind of computer generated hologram, which is a coordinate conversion hologram element obtained by dividing a hologram element into many sub-holograms using a computer and recording them on a photographic plate (H. Bartelt an.
d SKCase, ^" Coordinate transformations via multi
facet holographic optical elements ".OPTICAL ENGINE
RING, vol.22, No.4, pp.497-500 (1983)). Interferometer 1
The interference fringes obtained by the above are subjected to polar coordinate conversion by the coordinate conversion hologram 3 and detected by the detecting means 4, in the case of this embodiment, the CCD camera. The data captured by the CCD camera 4 is divided into 20 × 20 pixels on the computer 5, and each pixel is input to the neurons in the input layer of the neural network constructed by software on the computer 5.

As shown in FIG. 2, this neural network is of a type that uses a back-propagation learning rule in a hierarchical structure consisting of an input layer A, an intermediate layer B, and an output layer C. There are 400 input neurons because the 20 × 20 pixels are the inputs to the neuron. The number of intermediate layers B should be large to some extent, but in consideration of shortening the learning time, the number of intermediate layers B is set to four, and the neurons of the output layer C have a Z coefficient of Zernike polynomials up to the third order.
There are nine values from _{0 to} Z ₈ that can be determined.

In this neural network,
By inputting some interference fringes whose coefficients of the Zernike polynomial are already known, and learning is performed using the error backpropagation method so that the neuron of the output layer C corresponding to the polynomial fires at the value of the coefficient. The interference fringes generated from the Zernike coefficient were obtained by simulation, and the learning was performed using the obtained interference fringes. As simulation data for learning, Zernike polynomials Z _{0 to} Z ₈ appeared independently, and back propagation learning was performed for each case where the coefficients were 0.2, 0.5, and 0.8. Here, since Z ₀ is a constant term, it was excluded from the learning target. As an example, interference fringes when the Zernike coefficients Z ₈ are 0.2, 0.5 and 0.8 and the other coefficients are 0 are shown in FIGS. 3 (a), 3 (b) and 3 (c).

As a specific example, when the interference fringes shown in FIG. 4 when Z ₁ is 1.0 and Z ₈ is 0.5 are input to the wavefront aberration measuring device, Z ₁ is about 1.0. About 0.5 for Z ₈
Output was obtained.

In the present embodiment, the number of neurons in the output layer C is set to nine from Z _{0 to} Z ₈ , but in order to obtain higher-order (Z ₉ or more) coefficients, the neurons in the output layer C are It is clear that the number should be increased and the learning patterns should be increased accordingly.

Further, if it is necessary, even if the Zernike coefficient is converted into the Seidel coefficient, the conversion can be performed by a simple calculation as shown in the following Table 2, so that it is obvious that the processing time is hardly affected. .

[0019] Further, although it is not a method that is very impressive in terms of orthogonalization, it is of course possible to obtain Zernike coefficients or Seidel coefficients by using a neural network as it is in orthogonal coordinates without performing polar coordinate conversion or the like.

Further, in the above embodiment, the polar coordinate transformation is used as the coordinate transformation, but other polar coordinate transformations such as (x,
y) → (log (x ² + y ² ) ^1/2 , -tan (y /
x)) which is a combination of polar coordinate transformation and logarithmic transformation. The polar coordinate conversion hologram in this case may be created by the method using the sub-hologram described above.
ddle point method (M. Born and E. Wolf, "Principle of Opti
cs "(Pergamon, New York, 1965), p.753).

The wavefront aberration measuring device of the present invention has been described above based on the embodiments, but the present invention is not limited to these embodiments and various modifications can be made.

[0022]

As is apparent from the above description, according to the wavefront aberration measuring device of the present invention, the interference fringes obtained by the measurement are instantaneously coordinate-converted by the coordinate conversion hologram element, and the converted image is displayed. By inputting this input signal as an input signal to a neural network that has completed learning using data of known types and amounts of aberration, it is possible to perform complicated calculations as before for the input interference fringe information. Since it is not necessary to perform each time, the type and amount of aberration in the interference fringe can be instantly obtained.

[Brief description of drawings]

FIG. 1 is a diagram showing a schematic configuration of a wavefront aberration measuring instrument of one embodiment of a wavefront aberration measuring instrument of the present invention.

FIG. 2 is a diagram showing a configuration of a neural network.

FIG. 3 is a diagram showing an example of interference fringes used for learning of a neural network.

FIG. 4 is a diagram showing an example of interference fringes of a measurement target.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Interferometer 3 ... Coordinate conversion hologram element 2 ... Wavefront including interference fringes 4 ... Detection means 5 ... Computer A ... Input layer B ... Intermediate layer C ... Output layer

Claims (2)

[Claims] 1. A hologram element that performs coordinate conversion on interference fringes generated by a reference wavefront and an object wavefront from an object to be inspected, and an image converted by the hologram element as an input signal, and receives the signal. Intermediate of one or more layers consisting of an input layer consisting of multiple neuron groups and a neuron group that receives the excitation patterns of the neuron groups in the previous layer and performs pattern conversion and then outputs the excitation pattern to the next stage A wavefront aberration measuring instrument having a neural network including a layer and an output layer that receives and converts the excitation pattern of a final neuron in the intermediate layer and outputs the transformed pattern. 2. The neural network is adapted to input a plurality of pieces of interference fringe information of which types and amounts of aberrations are known, and to determine the size of neuron coupling between layers by error backpropagation learning. The wavefront aberration measuring device according to claim 1, which is characterized in that.