JPS63140934A - Analyzing method for shearing interference fringes - Google Patents

Abstract

PURPOSE:To reduce a shearing quantity and to reproduce the wave front of even shearing interference fringes whose wave front shift in phase large spatially by increasing the number of spatial samples of interference fringe intensity. CONSTITUTION:Laser light 1a emitted by a laser light source 11 is reflected by a body 15 to be measured and made incident on a shearing interferometer after phase modulation, and the interference fringe intensity is converted by a photoelectric element 19 into an electric signal. A triangular wave of angular frequency omega, on the other hand, is supplied to a driving circuit 211 for an electrostrictive element 17, and the output of the photoelectric element 19 is multiplied with clock pulses through an amplifier 212. The multiplication output is multiplied by a sine wave and a cosine wave synchronized with the output of a two-multiplier 24 and the outputs of low pass filters 28a and 28b are divided by a divider 29 to find the arctangent by an arctangent computing element 20. This operation is repeated by scanning interference fringes 10c in two dimensions by the photoelectric element 19 to find the whole phase of the interference fringes 10c, thereby finding the shape of the wave front of luminous flux 1b.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a measurement method for precisely measuring the shape of a flat, spherical or aspherical surface of a lens, mirror, etc., and specifically relates to a shearing interference fringe analysis method. .

BACKGROUND OF THE INVENTION Conventionally, in a fringe scanning type shearing interferometer, the amount of shearing depends on the spatial variation of the phase of the wavefront to be measured, and is also limited by the number of spatial samples of interference fringe intensity.

The prior art will be explained below using FIG. 7. The laser beam 6a emitted from the laser light source e1 is reflected by the measuring object 66 via the beam expander 82, half mirror 63a, and reference lens e4, and is phase modulated, changes the optical path by the half mirror 63a, and enters the shearing interferometer. .

The luminous flux 8b is a luminous flux ea at the half mirror e3b.

It is divided into 6d, subjected to relative lateral shift by the corner cubes 86a and 66b, and again... - Fumin-63b
'i causes interference fringes 6e. Here, the wavelength of the laser is λ
, when n is an arbitrary natural number, the corner cup 66a
is moved by 7 in the direction of the arrow using the electrostrictive element 67 to 6d.
The intensity of the interference fringes 6e is sampled at each phase by the imaging device #6a, and is captured in the frame memory 610. Here, the corner cue λ
i Intensity 1 of interference fringe 6e when professional 8a moves by 1f
(x, y, i,) is the phase of the wavefront of the light beam 6b h(
"z7), the amount of lateral shift in the X direction is ΔI, and the luminous flux is 6c.

6d amplitude respectively A1.6d. A2, where φ is the initial phase difference, it is given by the following equation.

1 (x, y, i) = 7 (A, +A2) + A, A
2cos (h(x, y)-h(technical or Δtechnical, a)-φ-
21) Therefore, using the Fourier series, the wavefront Δh (
x, y) are determined by the following formula.

Next, h(:c, y) is obtained by integrating Δh(x, y) in the X direction, performing the same process in the y direction, and synthesizing. Here, the lateral shift amount ΔX needs to satisfy the following equation.

1h(x, y)-h(x+Δ!, 7)l≦/7 ,,
, Kawa, , Yamamagari■Also, the number m of samples in the X direction by the imaging device 6a must satisfy the following equation, where D is the diameter of the light beam 6b.

77≦m・・・・・・・・・・・・Old old old old・
...Old... ■Problems to be solved by the invention In the conventional method described above, if the phase of the wavefront of the light beam 6b changes spatially significantly, it is necessary to reduce ΔX according to the formula (■). , Therefore, m is larger than in equation (2), which has drawbacks such as an increase in the capacity of the frame memory 61o and a slow calculation time. In addition, the number of samples m is limited by the performance of the imaging device,
It could not be made infinitely large. For these reasons, aspherical lenses with a large amount of aspherical surface could not be measured.

Means for Solving the Problems In order to solve the above problems, in the shearing interference fringe analysis method of the present invention, the phase of the laterally shifted wavefront and the phase of the other wavefront are relatively modulated in a triangular wave manner, Detecting the interference fringe intensity at one point of the interference fringes caused by shearing interference with a photoelectric element, and multiplying the output signal by a sine wave and a cosine wave twice the frequency of the triangular wave every half period of the triangular wave, respectively, After passing through a low-pass filter, the signal obtained by fully multiplying the sine wave is divided by the signal obtained by multiplying the cosine wave, and the phase of the interference wavefront at that point is obtained by calculating the arctangent of the signal. The phase of the entire interference wavefront is determined two-dimensionally over the entire area, and the original wavefront is reproduced based on that information.

Effect According to the above method, even in shearing interference fringes of a wavefront whose phase changes significantly spatially, by increasing the number of spatial samples of the interference fringe intensity, the amount of shearing can be reduced and the interference fringes can be improved. This enables analysis and wavefront reproduction.

EXAMPLES Below, examples of the present invention will be explained based on FIGS. 1 to 6. Laser light 1a emitted from a laser light source 11 such as a He-N e laser light source is reflected by a measuring object 16 via a beam expander 12, a half mirror 13a, and a reference lens 14, and is position-phase modulated. The optical path is changed and the beam enters the shearing interferometer. The light beam 1b is divided by a half mirror 13b, and is divided into corner cubes 18a and 18b.
The horizontally shifted upper receiver passes through the half mirror 13b again and becomes a shearing interference wavefront 1oc, and the photoelectric element 19 converts the interference fringe intensity into an electrical signal.

Furthermore, an electrostrictive element 17 is used to apply phase modulation to the optical path length. At this time, the output signal V(x
, y) is the phase 'kh(x, y) of the wavefront of the light beam 10b
, the amount of lateral shift of the light beams 10a and 10b is ΔI, the phase difference due to the difference in optical path length is φ, and the phase difference given by the electrostrictive element 1 is 4.
Then, it is given by the following formula.

V (z, y) = v1 + v2 cos (h (z, y) - h
(x+Δ!+7)-φ-4) Next, the clock pulse generator 23 generates a waveform 61 with an angular frequency ω (Fig. 5), and the triangular wave generator 22 generates a triangular wave with an angular frequency ω synchronized with this. and is supplied to the electrostrictive element drive circuit 211.

At this time, the phase l given by the electrostrictive element 17 is the waveform 31
The electrostrictive element drive circuit 211 is adjusted so that (FIG. 3) is obtained. At this time, the waveform of the output signal of the amplifier 212 becomes a waveform 41 (FIG. 4). This waveform 41 and waveform 61 are multiplied by a multiplier 25a to obtain a waveform 42 (FIG. 6). Next, a clock pulse with an angular frequency of 2ω is generated using a doubler 24, and a sine wave and a cosine wave with an angular frequency of 2ω synchronized with this signal are generated using a sine wave generator 26 and a cosine wave generator 27, The waveform 42 is multiplied using multipliers 25b and 25c, respectively, and low-pass filters 28a and 28
Integrate by b. The value of the low-pass filter 28a is divided by the value of the low-pass filter 2abO using the divider 29, and the arctangent is obtained using the arctangent calculator 20. As a result, the phase h(x,y)−h(x+Δ”t7)−φ is obtained.
The phase of the entire interference fringe IQc is determined by two-dimensional scanning as shown by arrows X and Y in FIG. In other words, based on the sharing amount ΔX! Integrate in the direction.

The shape of the wavefront of the light beam 1b can be determined by performing the same process in the y direction and combining the results with the results in the I direction.

Effects of the Invention As stated above, according to the present invention, since the photoelectric element scans the interference fringes two-dimensionally, the number of spatial samples can be freely increased, and the amount of shear can thereby be reduced. This makes it possible to measure the shape of a wavefront with a large phase change. Furthermore, since the phase at each point of the interference fringes can be calculated in an analog manner, measurement can be performed at high speed and with high precision.

[Brief explanation of the drawing]

FIG. 1 is a schematic diagram showing an embodiment of the present invention, FIG. 2 is a block diagram thereof, and FIGS.
Graphs showing signal waveforms of each block in FIG. 2 and FIG.
FIG. 7 is a schematic diagram showing a conventional example. 10c...Interference fringes, 11...Laser light source, 18a. 16b... Corner cube, 17...
Electrostrictive element, 19...Photoelectric element, 2o...
・Arcade tangent calculator, 22... Triangular wave generator, 23
...Clock Tsuku Sith Generator, 24...
- Double multiplier, 28a, 28b...low pass filter, 29...divider. Name of agent: Patent attorney Toshio Nakao and one other person
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Claims (1)

[Claims] In a fringe scanning type shearing interferometer, the phase of a laterally shifted wavefront and the phase of the other wavefront are relatively modulated in a triangular wave manner, and a photoelectric element detects the intensity of the interference fringe at any point in the interference fringes caused by shearing interference. , the output signal of the photoelectric element is multiplied by a sine wave and a cosine wave having a frequency twice the frequency of the triangular wave every half period of the triangular wave, and after passing through a low-pass filter, the signal multiplied by the sine wave is obtained. Dividing by the signal obtained by multiplying the cosine wave and calculating the arctangent of that signal determines the phase of the interference wavefront at that point.This operation is performed two-dimensionally over the entire interference wavefront to determine the phase of the entire interference wavefront. , a shearing interference fringe analysis method characterized by reproducing the original wavefront based on that information.