JPH04297808A - Error correction of phase shift fizeau interferometer - Google Patents

Abstract

PURPOSE:To reduce errors due to repetitive reflection by obtaining surface information of a test sample from the average of test phases obtained from two times of 4-interference fringe data pi/4 off in initial phase. CONSTITUTION:In the case of calculation by 4-point phase derivation algorithm, an error changes by a quadruple cycle of test phase: determining the average of two times of measurement pi/4 off in initial phase allows removal of errors. That is, with the initial phase set 0 deg. a 90 deg. phase shift is given to latch interference fringe data by repeating this scanning four times. Next, with the initial phase set 45 deg. interference fringe data is latched four times in the same manner. The result of first and second operations is obtained. As a result, the average of both cancels the respective errors from error characteristics carried by both.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for correcting errors in a phase shift Fizeau interferometer, and more particularly to a method for correcting errors caused by repeated reflections between a reference mirror and a surface of a sample to be measured.

0002

2. Description of the Related Art Interference microscopes using phase shift interferometry are attracting attention when measuring the fine surface shape of an object in a non-contact manner. This phase shift Fizeau interferometer 1
0, as shown in FIG. 5, the light emitted from the light source 12 is reflected downward in the figure by the beam splitter 14, a part of it is reflected by the reference mirror 16, and further reflected by the reference mirror 1.
The light that has passed through 6 is reflected by test sample 18 . and,
The reflected light from the reference mirror 16 and the reflected light from the test sample 18 are combined to generate interference light. Therefore, a phase shift is introduced into the interferometer to derive interference fringes, and the interference fringes at that time are detected by the camera 20 to obtain information on the surface shape of the sample.

In this phase shift interferometer, a four-point phase derivation algorithm is often used to obtain surface shape information. The four-point phase derivation algorithm is
In this method, one period of the interference fringes is divided into four, a phase shift of π/2 is applied to shift the interference fringes, and the phase is calculated from the data of the four interference fringes. That is, the test sample surface 18
Assuming that the reflectance of the reference mirror 16 is low and that the influence of secondary and higher-order repeated reflections can be ignored, the intensity distribution of interference fringes on the image plane can be expressed by the following equation 1.

0004

[Equation 1] I (x, y) = a (x, y) + b (x, y) c
os {φ(x, y)} where φ(x, y) is 2π・ω
(x, y)/λ, and ω(x, y) is the height distribution of the test surface. Therefore, by determining this ω(x, y), surface information of the test sample can be obtained. Also, a
(x, y) and b(x, y) can each be considered constants for specific points on the surface to be tested. Therefore, if a phase shift Δφ is introduced by some method, the above equation 1 can be replaced as shown in the following equation 2.

[0005]

[Formula 2] I (x, y, Δφ) = a (x, y) + b (x, y) co
s{φ(x, y+Δφ)} and the said Δφ is 0, π/
2, π, 3π/2, each intensity distribution I1
, I2, I3, and I4, φ(x, y) can be obtained from the following equation 3.

[0006]

[Formula 3] φ(x, y) = tan-1 {(I4-I2)/(I1-
I3)} Information on the surface to be inspected is obtained from this φ(x, y).

[0007]

However, in this phase shift interferometer 10, errors actually occur due to repeated reflections between the reference mirror 16 and the test sample 18. That is, as shown in an enlarged view in FIG. 6, multiple reflections occur between the reference mirror 16 and the test sample 18 for the incident light L, and each of the reflected lights L1, L2, L3, etc. causes a measurement error. It is.

[0008] As a method of reducing the influence of repeated reflections in the Fizeau interferometer, it is possible to insert an attenuator between the reference mirror of the interferometer and the test sample and absorb the light passing between them. However, attenuators are expensive, easily breakable, and require installation space.

Another possible method is to coat the reference mirror with an absorbing film to absorb the repeatedly reflected light. However, this method still has the problem that repeated reflections cannot be completely removed.

The present invention has been made in view of the problems of the prior art described above, and its object is to provide an error correction method for a phase shift Fizeau interferometer that can reduce errors caused by repeated reflections.

[0011]

[Means for Solving the Problems] In order to achieve the above object, the phase shift Fizeau interferometer according to the present invention calculates the phase error by averaging the results of two measurements in which the initial phase is shifted by π/4. It removes the That is, the correction method of the phase shift interference device of the present application is such that the initial phase is π/4.
The method is characterized in that 4 interference fringe data with a deviation of 2 degrees are collected and the surface information of the test sample is obtained from the average of the test phases obtained from each of the 4 interference fringe data.

0012

[Operation] The present inventors conducted an error analysis of the phase shift Fizeau interferometer as follows. That is, the intensity distribution of interference fringes when repeated reflections are considered is as shown in Equation 4 below.

[0013]

[Equation 4] I=1-b/{1-c・cos(Φ/4)} Note that b and c depend only on the reflectance of the reference mirror and the test sample, and are expressed by the following equations 5 and 6, respectively. As shown.

[0014]

[Formula 5] b=(1-r12)(1-r02)/(1+r12r2
2) r0: Amplitude reflectance of light at the interface between glass and film r1: Amplitude reflectance of light at the interface between film and air r2:
The amplitude reflectance of light depends on the surface of the sample being tested.

[0015]

[Math 6]c=2r1r2/(1+r12・r22)Math 6
, phase shift Δφ=0, π/2, π, 3π/2
given, the intensity distribution of the corresponding interference fringes is, respectively,

[0016]

[Formula 7] I1=1-b/(1-c・cosφ)I2=1
-b/{1-c・cos(φ+π/2)}=1-b/(
1+c・sinφ) I3=1−b/{1−c・cos(φ+π)}=1−b
/(1+c・cosφ) I4=1−b/{1−c・cos(φ+3π/2)}=
1-b/(1-c·sinφ). Using the phase calculation algorithm of number 3 above,

[0017]

[Formula 8] I4-I2=2bc・sinφ/(1-c2sin2φ
)I3-I1=2bc・cosφ/(1-c2cos2
φ). From this equation 8, the phase φ' can be determined as follows.

[0018]

[Formula 9] tanφ'=(I4-I2)/(I3-I1)
= tanφ−(1−c2cos2φ)/(1−c2
sin2φ) = tanφ+tanφ{(−
c2cos2φ)/(1-c2sin2φ)}This number is 9
from

[0019]

[Formula 10] tanφ'-tanφ=-c2tanφ{cos2φ/
(1-c2sin2φ)} Therefore, the error is small and φ'
When and φ are close,

[0020]

[Formula 11] sin(φ'-φ)≒-c2/2・sin2φ・cos
2φ/(1-c2sin2φ) =-c2/
4・sin4φ/(1−c2sin2φ), and furthermore, the reflectance between the reference mirror and the test sample surface is small, and r1, r
When 2<<1, c<<1, the error ε is ε=φ'-φ≒-c
It becomes 2/4・sin4φ. This is a sine function with a period four times that of the tested phase, as shown in FIG. Note that the intensity reflectance of the reference mirror in FIG. 7 is 25%, and the reflectance R2 of the test sample surface is 4%, 50%, and 90%.

The present inventors have completed the present invention in view of the characteristics of such errors. In other words, when calculated using the four-point method, the error changes at a period four times that of the tested phase, and this error can be reduced by taking the average value of two measurements with an initial phase shift of π/4. I decided to remove it.

[0022]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the basic configuration of a phase shift microfizeau interferometer according to an embodiment of the present invention. Note that parts corresponding to the prior art shown in FIG.
0 is added and the explanation is omitted.

The interferometer 110 shown in the figure includes a light source 112 made of a red semiconductor laser, a beam splitter 114, and a reference mirror 116. The laser beam emitted from the light source 112 is made into parallel light by a collimator lens 122, and further enters the beam splitter 114 via lenses 124, 126, and 128. The light reflected downward in the drawing by the beam splitter 114 is again made into parallel light by the objective lens 130, and further becomes circularly polarized light by the quarter-wave plate 132. Then, the circularly polarized light irradiates the reference mirror 116, and part of the light is reflected by the surface of the reference mirror 116, and the light transmitted through the reference mirror 116 is reflected by the test sample 118. As a result, the light reflected on the surface of the reference mirror 116 and the test sample 118
The reflected light is superimposed again by the reference mirror 116 to form interference light. Then, lens 13 again
0, passes through the beam splitter 114 and is guided upward in the figure. This light is imaged by the imaging lens 136 on the light receiving surface of the CCD camera 120.

The observation results by the camera 120 are displayed on the monitor 14.
0 and is visually observed by the frame memory 142.
After being subjected to desired data processing by the microcomputer 144, the data is output to the X-Y plotter 146.

Furthermore, in this embodiment, an injection current control command from the microcomputer 144 is given to the injection current control means 150 via the interface 148, and the injection power to the semiconductor laser 112 can be changed.
A temperature control means 152 controls the temperature of the semiconductor laser 112 to be constant.

That is, as the injection current i increases, the semiconductor laser changes wavelength λ in proportion to the increase in injection current i.
has a linear region where the value increases. In this example,
This characteristic property of semiconductor lasers is used to obtain surface information.

The above equation 1 can be rewritten as follows using the wavelength λ as a parameter.

[Formula 12] I (x, y, λ) = a (x, y) + b (x, y) cos
[{2π·2ω(x,y)+L}/λ0−Δφ] Then, by changing the above-mentioned Δφ, I1 to I4 are obtained. Note that L is the difference in optical path length between the reference mirror 116 and the surface of the test sample 118. Here, when the current injected into the semiconductor laser 112 is changed, not only the oscillation wavelength but also the laser intensity changes, so either the laser intensity is monitored and the intensity of the interference fringes is normalized, or the optical path difference of the interferometer is increased. This minimizes the change in the injection current required to obtain the required phase difference and minimizes the change in laser power. As a result, even when the laser wavelength is shifted as in the present invention, the bias a and amplitude b of the intensity distribution of the interference fringes shown in Equation 12 can be regarded as constant.

On the other hand, when the injection current i is changed and the oscillation wavelength is shifted from λ1 to λ2, the phases can be expressed as follows. λ1: φ1=2π・(L/2×2)/λ1
=2πL/λ1 λ2: φ2=2π・(L/
2×2)/λ2=2πL/λ2 Therefore, the phase difference Δφ=φ
2-φ1=2πLΔλ/λ12. For this reason, Δφ
It can be expressed as =2πLΔλ/λ2. That is, by varying the injection current i, the Δλ that becomes Δφ=2πLΔλ/λ2=0 Δφ=2πLΔλ/λ2=π/2 Δφ=2πLΔλ/λ2=π Δφ=2πLΔλ/λ2=3π/2 is determined by changing the injection current I1,
All you have to do is obtain I2, I3, and I4.

By the way, since the amount of change in wavelength Δλ is proportional to the change in injection current Δi, Δλ=α・Δi, that is, 2πLΔλ/λ2=2πLαΔi/λ2=2π
Taking the case of Δi=λ2/Lα as an example. For a typical red laser, 670 at 20℃
Since α=0.017 nm/mA for the standard wavelength of nm, if L=24 mm, the current change required for a change of 2π is Δi (mA) = (670×10-3)2/(24 ×0.
017)=1.100mA.

Therefore, the injection currents of π/2, π, and 3π/2 are respectively 0.275 mA, 0.550 mA, and 0.
It is sufficient to change it by 825 mA. Since the linear region of a semiconductor laser is about 10 mA, it is easy to change the current to this extent. As described above, in this embodiment, a desired phase difference is obtained by controlling the current injected into the semiconductor laser 112, so extremely accurate phase control is possible.

The characteristic feature of the present invention is that when calculated using the four-point method phase derivation algorithm, the error changes at a period four times that of the tested phase, and two times with an initial phase shift of only π/4. This error is removed by taking the average value of the measurements. That is, FIG. 2 shows a flowchart of an error correction method according to an embodiment of the present invention. As is clear from the figure, upon starting the measurement, the initial phase is set to 0, a 90° phase shift is applied, interference fringe data is acquired, and this scanning is repeated four times to obtain I1 to I4.

Next, the initial phase is set to 45°, a phase shift of 90° is given, interference fringes are captured, and this scanning is repeated four times to obtain I5 to I8. Then, first, the above I1 to I4
Based on

[0033]

[Formula 13] Φ1=tan-1 {(I3-I1)/(I4-I2)}
Calculate. Next, based on the above I5 to I8,

003
4]

[Formula 14] Φ2=tan-1 {(I7-I5)/(I8-I6)}
Calculate -π/4. Then, the average of the obtained Φ1 and Φ2 is obtained. Φ=(Φ1+Φ2)/2

As a result, as shown in FIG. 3, when Φ1 has an error characteristic as shown by the solid line in the figure, Φ2 has an error characteristic as shown by the dotted line in the figure, and the average value of both is exactly This will cancel out the errors in Φ1 and Φ2. Although this embodiment requires returning the shifted state after measuring I4, it has the advantage of being easily applicable to currently used phase shift interferometers.

FIG. 4 shows a flowchart of an error correction method according to a second embodiment of the present invention. In this example, the measurement is performed by applying a phase shift of 45 degrees at the beginning of the measurement.
Data is obtained in the order of 7, I4, and I8. Then, Φ1 and Φ2 are obtained using Equations 13 and 14, and the average of the two is taken. In this embodiment, since phase data is obtained continuously from the beginning, there is an advantage that there is no need to return the shifted state.

As explained above, according to the phase shift interferometer according to each of the above embodiments, the four-point method is performed twice with a phase shift of π/4, and the average of both is taken.
It becomes possible to obtain accurate surface information of a test sample without adding any special configuration to a conventional device.

Furthermore, according to the micro-Fizeau interferometer according to this embodiment, since there is no mechanically movable part such as a piezo element, the system is stabilized, and even measurements with a phase shift of π/4 are extremely accurate. It is possible to respond accurately. still,
In this example, a method is used to control the current injected into the semiconductor laser in order to give a phase shift. However, like a general phase shift interferometer, a method of moving a reference mirror using a piezo element etc. is used. Good too.

[0039]

Effects of the Invention As explained above, according to the phase shift microfizeau interferometer according to the present invention, the four-point method can be
Since the measurement was performed twice with a four-phase shift and the average of both results was taken, surface information with few errors can be obtained with a simple configuration.

[Brief explanation of drawings]

FIG. 1 is a diagram illustrating the configuration of a phase shift Fizeau interferometer according to an embodiment of the present invention.

FIG. 2 is a flowchart schematically showing the steps of the correction method according to the first embodiment of the present invention.

FIG. 3 is an explanatory diagram of the operation of the correction method according to the first embodiment.

FIG. 4 is a flowchart showing the general steps of a correction method according to a second embodiment of the present invention.

FIG. 5 is an explanatory diagram of a general phase shift interferometer.

[Figure 6],

FIG. 7 is an explanatory diagram of problems with a conventional phase shift interferometer.

[Explanation of symbols]

12,112 Semiconductor laser 16,116 Reference mirror 18,118 Test sample

Claims (1)

[Claims] 1. A reference mirror that reflects a part of the light emitted from the light source, a test sample that reflects the other part of the light emitted from the light source, and a reference mirror that reflects the light reflected from the reference mirror and the sample. and a synthesizing means for synthesizing the reflected light from and generating interference light, and by obtaining the test phase from four pieces of interference fringe data whose phase is shifted by π/2 of the interference fringes, surface information of the test sample is obtained. In a phase shift Fizeau interferometer, 4 interference fringe data of 2 degrees with the initial phase shifted by π/4 are collected, and the surface information of the test sample is determined from the average of the test phases obtained from each of the 4 interference fringe data. A method for correcting errors in a phase-shifted Fizeau interferometer, characterized by obtaining the following: