JPH0437362B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Field of Application of the Invention] The present invention relates to a method and apparatus for measuring the surface shape or surface position of an object to be measured.

[Prior art]

Conventionally, as a method of measuring the surface shape of a workpiece, a Twyman-Green interferometer or a Huizou interferometer is used to determine the surface shape of the workpiece from the shape of the interference fringe pattern generated by the reference light and the workpiece. The method is widely used.

In addition, as a method to improve measurement accuracy, the change in the intensity of the interference pattern that occurs when the light wave phase of the reference light or object light is changed is determined at sample points on the interference pattern, and the change in the intensity of the object light when the intensity is the minimum is determined. A method is used in which the amount of change in the phase of a light wave or the phase difference in a sinusoidal change in the intensity of an interference pattern is determined at each sample point.

As the latter method, it is possible to use complex fast Fourier transform (hereinafter abbreviated as FFT), but the values obtained by FFT are frequency components (complex numbers) at discrete frequency sample points.

Therefore, unless the amount of input data becomes very large, the interval between discrete frequency sample points will be large, and the phase will be calculated using only the data for which the absolute value of the value at the discrete frequency sample points obtained by FFT is maximum. When calculating the value, sufficient measurement accuracy cannot be obtained.

In order to avoid this, if we increase the number of input data, that is, if we try to change the optical wave phase in many stages and use a large number of measurement data, it not only takes a huge amount of measurement time and calculation time, but also takes a long time. There is also a problem in that the influence of disturbances on the measurement time over time cannot be ignored.

[Purpose of the invention]

An object of the present invention is to provide a measuring method and apparatus that can measure the surface shape or surface position of an object to be measured in a short time and with very high precision, and that can perform measurements that are relatively resistant to disturbance conditions. It's about doing.

[Summary of the invention]

In order to achieve the above object, the present invention divides light obtained from a coherent light source into two, changes the optical path length of one of the two divided optical paths, modulates the optical wave phase, and modulates the optical phase of one of the two divided optical paths. Light is irradiated onto the object to be measured, and the light reflected or transmitted from the object to be measured and the reference light obtained by irradiating the reference surface with the other light divided into two are measured within the range in which the wavefronts of both lights are measured. Interfering so that they almost match and generating an interference pattern,
N intensity distributions at a plurality of desired sample points in the space of the interference pattern are determined and stored as N discrete data that changes sinusoidally in accordance with the temporal change in the optical path length; The N pieces of discrete data at each point are subjected to discrete Fourier transform, and the Fourier transform data gives a frequency corresponding to the period of the sine wave in the absolute value of the discrete Fourier transform data obtained by the Fourier transform. This measurement method is characterized in that information on the sinusoidal component of the interference pattern is obtained by interpolating the values of the discrete Fourier transform data at the maximum sample point and the sample points adjacent thereto. In the present invention, the intensity distribution of N interference patterns obtained when the optical wave phase of either the light from the object to be measured or the reference light is changed N times is recorded, and from each sample point on this interference pattern Perform discrete complex FFT on the extracted discrete data, and correspond to the discrete frequency where the absolute value of the N pieces of discrete complex Fourier transform data obtained by FFT is the maximum, and the discrete frequencies before and after that frequency. The feature is that the complex number Fourier transform data obtained by the method is interpolated, the phase of the interference pattern at each sample point is determined, and the surface shape of the object to be measured is thereby measured.

[Embodiments of the invention]

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 1 shows an embodiment of a surface profile measuring device according to the present invention.

In the figure, light emitted from a coherent light source 1 such as a laser is turned on and off by a high-speed shutter 2.
Beam expanding optical system 3 for light passing through high-speed shutter 2
The beam is expanded to a desired beam diameter, and is separated into two optical paths 5 and 6 by a beam splitter 4. An object to be measured 7 is installed in the optical path 5, and when the object to be measured 7 has a spherical surface, a focus lens 8 is installed.
is inserted. This focus lens 8 focuses the incident expanded parallel beam to one point.
If the object to be measured 7 is installed so that this focal point and the center of curvature of the object to be measured 7 as a spherical mirror coincide,
The light reflected by the object to be measured 7 passes through the focus lens 8 again, becomes a parallel beam, and returns to the beam splitter 4.

The optical path 6 of the other beam separated by the beam splitter 4 serves as a reference optical path, and a wedge glass 9 is inserted into this reference optical path, and this wedge glass 9 is moved by a constant pitch by a drive mechanism 10. .
The beam that passes through the wedge glass 9, is reflected by the reflection mirror 11, passes through the wedge glass 9 again, and returns to the beam splitter 4.

The beam returned from the object to be measured 7 and the beam converted from the reference optical path interfere in the interference pattern generation optical path 12. This interference pattern is projected onto the imaging surface 15 of the imaging device 14 by the imaging lens 13.
The imaging lens 13 is arranged to substantially form an image of the object to be measured 7 on an imaging surface 15 .

As shown in FIG. 2, the imaging surface 15 has imaging sample points that are effectively divided into L×L pieces, and the interference pattern 30 is sampled at a constant pitch, and the interference pattern intensity at each imaging sample point is It is detected and sent to the control circuit 16.

The control circuit 16 moves the wedge glass 9 intermittently at a constant pitch, opens the high-speed shutter 2, and captures the interference pattern intensity signal obtained by the imaging device 14. In this way, by moving the wedge glass 9 N times, N interference pattern intensity signals are captured, converted into analog/digital data, and stored in the external memory 18 via the computer 17.

For the t _i- th position of the wedge glass 9, the interference pattern intensity at address (l, m) on the imaging surface 15 is calculated.
If I _l , _n (t _i ), the wedge glass 9 moves at a constant pitch, so for example, the intensity signals at points A and B on the imaging plane in FIG. 2 are I A and _I in FIG. 3, respectively.
Change like I _B. A similar intensity change is obtained for all sample points of the interference pattern generating section on the imaging surface 15, and the relative phase difference of this sinusoidal intensity change represents the surface shape of the object to be measured. Therefore, it is only necessary to find the phase of the sinusoidal intensity change.

From a large amount of data stored in the external memory 18, only N pieces of data at addresses (l, m) are taken out to the computer 17, and are sent to the FFT calculation circuit 19,
For example, if you input a complex number into an array processor,
Perform FFT calculation.

That is, the discrete Fourier transform shown in the following equation is performed.

O _l,n (f _k )= _N-1 〓 ^ti=0 I _l,n (ti) _exp j2πtifk/N ………(1) (j: imaginary number, ti, f _k =0,1,2,… ..., N-
1) The results obtained by discrete Fourier transform are as shown in Figure 4a or Figure 4b.

FIG. 4a shows a case where the original interference pattern intensity is reproduced when the wedge glass 9 is intermittently fed a certain number of times. In other words, the amount of phase modulation △φ due to one time of intermittent feeding by the wedge glass is 2π/L (L: integer)
This is the case expressed as. In this case, f _p , f _k ,
At all sample points except f _N-1-k , the absolute value |O(f)| of the discrete data O(f) is close to 0, and the phase of the complex number Of _k , that is, the phase of the data Of _k The arctangent of the real part divided by the imaginary part of the data O( _fk ) becomes the surface shape phase to be sought.

However, in general, the above L is not an integer. In this case, |O(f) at points other than f _k and f _p
| is not 0, and the value corresponding to the frequency of the sinusoidal change in the interference pattern is as shown in Figure 4b.
The point f _k ' (f _{k '} is not an integer) is shifted from the point f k where the absolute value of the FFT discrete data O(f ₎ is maximum.

Therefore, it is necessary to find this point f _k ' and find the phase of data O(f) at that point. wedge glass 9
The light wave phase change △φ caused by one movement of
Let 2π ^k0/N . Here, N is the number of interference patterns to be imaged, k ₀ is a real number, and it is assumed that the following equation is satisfied.

k ₀ = k ₁ +△k ………(2) (k ₁ : integer, |△k|≦0.5) Also, if the phase of address (l, m) is φ(l, m), the interference pattern is The intensity I _l,n (t _i ) is given by the following equation.

I _l,n (t _i ) =a ₀ +a ₁ cos {2πk ₀ /Nt _i +φ(l, m)}...
(3) t _i = 1, 2, 3, ..., N, a ₀ ≧a _1Only when the light from the object to be measured and the reference light are equal,
Although a ₀ = a ₁ , it is generally designed so that a ₀ > a ₁ .

The result of executing FFT matches the result of substituting equation (3) into equation (1), so the following equation is obtained.

O _l,n (f _k )=a ₀ exp (iπf _k N-1/N) sinπf _k /sinπ
f _k /N+a ₁ [expi{φ(l,m) +π(f _k +k ₀ )N-1/N}] sinπ(f _k +k ₀ )/sin
πf _k +k ₀ /N+expi{−φ(l,m)+π(f _k −k ₀ )N
−1/N}sinπ(f _k −k ₀ )/sinπf _k −k ₀ /N ………(4) When N is large, the first term of this equation (4) is the delta function δ(f _k ) , regardless of the size of N, f _k =
0 for N, and 0 for other integers f _k (0≦f _k ≦N-1). When N is large, the second and third terms are proportional to the delta functions δ(f _k +k ₀ ) and δ(f _k −k ₀ ), respectively, and regardless of the size of N, f _k =±k ₀
becomes N. Therefore, when k ₀ is an integer, Fig. 4a
When k ₀ is not an integer, the result will be as shown in Figure 4b. As shown in Figure 4b, the result obtained by FFT is that f _k is an integer value, so f _k
The value of data O _l,nf(k) at =±k ₀ (k ₀ ≠ integer) is not directly output.

However, since the phase (phase difference) of the data O _l,n (f _k ) at f _k = k ₀ at address (l, m) represents the surface shape, the computer 17 executes the following calculation process. do.

(1) Since the amount of movement of the wedge glass is known in advance with some degree of accuracy, the integer k ₁ in equation (2) is known.
Therefore, for this k ₁ , the data O _l,n(fo) when △k is changed from -0.5 to 0.5 in constant steps is
The phase Ψ(△k, φ) of is determined by the following equation.

Ψ(△k,φ) =tan ^-1 [I _n {O _l,n (k ₁ +△k)}/Re{O _l,n (k ₁
+△k)}]……(5) (2) Similarly, when △k and φ(l, m) are changed as described above, R given by the following equation (6) is Make it a table.

R(△k,φ) =｜O _l,n (k ₀ +S)｜/｜O _l,n (k ₀ )｜ ………(6) However, here, S satisfies the condition of the following equation. shall be met.

｜O _l,n (k ₀ +S)｜≧｜O _l,n (k ₀ −S)｜｜S｜=1 ………(7) (3) Among the N measured interference pattern data Result of FFT of N pieces of data at address (l, m)
The absolute value of O _l,n (f _k ) is maximum, f _k ≠ 0, _{f k}
Find it in the range ≦N/2, and let f _k at that time be k ₀ .

From this FFT result, O _l,n at f _k = k ₀
Find the phase Ψ(k ₀ ) of (f _k ) and the following equation.

R'=｜O _l,n (k ₀ +S)｜／｜O _l,n (k ₀ )｜......(
8) However, S is given by equation (7).

That is, k ₀ +S is the sample point of the FFT output that is next to k ₀ and has the second largest absolute value.

Using the previously created table shown in Figure 5,
If we calculate △k and φ(l ₀ ) that match φ(k ₀ ) and R′ from the table, then φ(l ₀ )
becomes the desired phase.

In addition, when carrying out the processing in paragraph (3) above,
If the values of Ψ(Δk, φ) and R(Δk, φ) in the table are interpolated, it becomes possible to obtain the values with even higher precision.

By performing the processes (1) to (3) over all addresses where the interference pattern of the object to be measured appears, the shape of the object to be measured can be determined.

The surface shape of the object to be measured obtained in this way is not always accurate due to the fact that the measurement optical system shown in Figure 1 itself is not equipped with a perfect plane mirror, a safe beam splitter, or a focus lens. However, it does not represent accurate surface profile measurement results.

In such a case, prior to measuring the object to be measured, a highly accurate prototype (a spherical prototype in FIG. 1) is used as the object to be measured, and the measurement is carried out in the same manner as described above. The measurement results represent imperfections (distortions) in the measurement optical system itself, so
If this measurement result is used as a correction value for any subsequent spherical surface measurement, any spherical surface can be measured with high precision using the accuracy of the spherical prototype as the absolute measurement accuracy.

In the example shown in FIG. 1, the object to be measured is a spherical surface, but if the focus lens is removed, it is possible to measure a flat object.

In addition, although the example in Figure 1 shows a reflective object to be measured, if a Mach-Zender interferometer is used, the characteristics of lenses and transmission optical components can also be measured in the same way. It becomes possible.

As can be seen from the above embodiments, highly accurate measurement results can be obtained from data obtained by performing discrete complex fast Fourier transform on the intensity data of a relatively small number of N interference patterns. Not only is it possible to measure the surface shape with extremely high accuracy within a short processing time, but the effects of external disturbances can also be ignored.

Another object of the present invention is to enable highly accurate measurement even if the light wave modulation step of the light wave modulation of a phase modulator such as a wedge glass is not a specific value. That is, while the conventional method had an accuracy of several tens of λ, the present invention can achieve an accuracy of several hundred λ.

Furthermore, in order to achieve such high-precision measurements, conventional methods require very stable fixation of the measurement optical system and object to be measured, as well as air fluctuations in the optical path of the object to be measured and the reference optical path. However, in the example described above, stability is not required for things that change linearly within the measurement time, so even if the conditions required for the measurement optical system are loose, high precision measurement is possible. becomes possible.

〔Effect of the invention〕

As described above, according to the present invention, the surface shape or surface position of the object to be measured can be measured in a short time and with high precision, and the surface shape or surface position can be relatively resistant to disturbance conditions. Can be measured.

[Brief explanation of drawings]

The figures are all related to embodiments of the present invention. Fig. 1 is a configuration diagram of an embodiment of the measuring device, and Fig. 2 shows the interference pattern on the imaging surface of the imaging device shown in Fig. 1 and the imaging sample point. Figure 3 is a diagram showing the arrangement, Figure 3 is a diagram showing intensity changes on sample points of the interference pattern, and Figures 4 a and b are diagrams showing intensity changes on sample points of the interference pattern.
A diagram showing the FFT results, and FIG. 5 is a diagram showing a table for determining the phase value. DESCRIPTION OF SYMBOLS 1... Coherence light source, 8... Measured object, 9... Wedge glass, 14... Imaging device, 15... Imaging surface, 16... Control circuit, 17... Computer.

Claims (1)

[Claims] 1. Light obtained from a coherent light source is divided into two, the optical path length of one of the two divided optical paths is changed to modulate the optical wave phase, and one of the light is directed to the object to be measured. The light reflected or transmitted from the object to be measured and the reference light obtained by irradiating the reference surface with the other divided light are made so that the wavefronts of both lights almost match within the range to be measured. to generate an interference pattern, and N intensity distributions at a plurality of desired sample points in the space of the interference pattern are determined by N discrete intensity distributions that vary sinusoidally in accordance with temporal changes in the optical path length. N pieces of discrete data at each of the stored points are subjected to discrete Fourier transform, and the period of the sine wave in the absolute value of the discrete Fourier transform data obtained by the Fourier transform is Information on the sinusoidal component of the interference pattern is obtained by interpolating the values of the discrete Fourier transform data at the maximum sample point of the Fourier transform data giving a frequency corresponding to the frequency and the sample point adjacent thereto. measurement method. 2 The light obtained from the coherent light source is divided into two, one of the lights is irradiated onto the object to be measured, and the light that is reflected or transmitted from the object to be measured and the light that is reflected or transmitted from the other of the above-mentioned two halves. N intensity distributions of interference patterns with the other light obtained as a reference light to be interfered with are obtained by changing the light wave phase of either the light from the object to be measured or the reference light N times and stored. , discrete complex Fourier transform is performed on N pieces of discrete data taken from one sample point on the interference pattern, and the absolute value of the N pieces of discrete complex Fourier transform data obtained by the discrete complex Fourier transform is the maximum. A measurement method characterized by interpolating discrete complex Fourier transform data corresponding to a discrete frequency and a discrete frequency adjacent to the frequency to determine the phase of the interference pattern at the sample point. 3. A coherent light source, a separation means for separating the light from the light source into two optical paths, a modulation means for modulating the optical wave phase by changing the optical path length of one of the two optical paths, and 2. irradiation means for irradiating the object to be measured with one of the two optical paths; reference light means for irradiating the other divided light onto a reference surface to obtain a reference light; and the object to be measured irradiated by the irradiation means. generation means for generating an interference pattern by guiding the light reflected or transmitted from the reference light and the reference light obtained from the reference light means into one optical path so that the wavefronts of both lights almost match within the measurement range, causing interference; and,
N intensity distributions at a plurality of desired sample points in the space of the interference pattern generated by the generation means are changed sinusoidally in accordance with temporal changes in the optical path length modulated by the modulation means. a detection means for detecting as discrete data, a storage means for storing intensity distributions of N interference patterns detected as N discrete data by the detection means; Fourier transform means for performing discrete Fourier transform on N pieces of discrete data;
The discrete Fourier transform at the sample point at which the Fourier transform data has a maximum and the sample point adjacent thereto that gives a frequency corresponding to the period of the sine wave in the absolute value of the discrete Fourier transform data obtained by the Fourier transform means. A measuring device comprising: measuring means for interpolating data values to obtain information on the sinusoidal component of the interference pattern. 4 A coherent light source, a separation means for separating the light from the light source into two optical paths, an irradiation means for irradiating one of the two optical paths onto the object to be measured, and a light wave of the other light of the two optical paths. a modulating means for modulating the phase;
a generating means for generating an interference pattern by guiding the two optical paths into one optical path; a detecting means for detecting the intensity of the interference pattern generated by the generating means at a sample point; A storage means for storing the intensity distribution of N interference patterns when the light wave phase is modulated N times, and N intensity signals at predetermined sample points are taken out from the patterns stored in the storage means and subjected to discrete complex Fourier transformation. and a Fourier transform means for interpolating the Fourier transform data corresponding to a discrete frequency at which the absolute value of the discrete complex Fourier transform data obtained by the Fourier transform means is maximum and a discrete frequency adjacent to the frequency. A measuring device comprising: measuring means for determining the phase of an interference pattern at a sample point. 5. The measuring device according to claim 4, wherein the modulating means includes a wedge-shaped glass and a means for moving the glass by a constant minute amount.