JP3441508B2 - Phase detection method in semiconductor laser phase shift interferometer - Google Patents

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for detecting a phase in a phase shift interferometer using a wavelength modulation characteristic of a semiconductor laser. 2. Description of the Related Art For example, reflected light from the surface of an object to be measured and light reflected from a reference surface (reference mirror) interfere with each other, and the phase distribution of the interference fringes causes the interference between the reflected light and the object to be measured. Methods for measuring the surface profile are widely known. Also,
A fringe image analysis technique that focuses on the phase when the interference fringes change temporally or spatially has also been proposed. For example,
When the reference mirror is moved while being orthogonal to the optical axis to apply phase modulation to the fringe image, the surface shape of the object can be measured from at least three pieces of fringe image information (phase shift method). Further, instead of moving the reference mirror, the phase of the reflected light from the surface of the test object and the phase of the reflected light from the reference mirror are shifted by changing the oscillation wavelength by changing the injection current to the semiconductor laser. Semiconductor laser phase shift interferometers have been proposed. This interferometer has the excellent feature of having no moving parts. [0004] These phase shift methods are methods for obtaining a phase at a specific phase point based on a plurality of measured values obtained by changing the phase. When this specific phase point is called a reference phase point, At least during the measurement at several points before and after the reference phase point, the light intensity does not fluctuate, and the addition of the phase shift amount as assumed in advance is a prerequisite for establishing the measurement with high accuracy. However, in a semiconductor laser, if the injection current is changed to change the oscillation wavelength, not only the phase but also the light intensity changes, and the phase of the fringe image cannot be determined accurately. Further, there is a problem that the ratio of the amount of phase shift to the amount of change of the injection current is not always the ratio expected in advance. An object of the present invention is to provide a semiconductor laser phase shift interferometer for controlling an injection current to a semiconductor laser to change its oscillation wavelength even if the light intensity changes or there is a phase shift deviation. It is an object of the present invention to obtain a phase detection method capable of correctly obtaining a phase at a reference phase point by removing the fluctuation, and in particular, to obtain an algorithm for calculating a phase distribution. SUMMARY OF THE INVENTION The present invention is an interferometer using a semiconductor laser as a light source, a wavelength shift means for changing an oscillation wavelength of the semiconductor laser, and a device for inputting fringe image information resulting from interference. A phase detection method in a semiconductor laser phase shift interferometer having: a fringe image input unit having a two-dimensional pixel group; dividing a 2π phase space into m (m ≧ 3) measurement phase points; While shifting the oscillation wavelength of the semiconductor laser by the wavelength shifting means, fringe image information is obtained at each measurement phase point, and a total of n pieces of fringe image information I _i (n ≧ 2)
m-1; m ≧ 3, i = 0~n-1, I i obtains the light intensity) of each two-dimensional pixel group n pieces of fringe image information step and; fringe image information _{I i} of the measured , G _j ; I _j ,
(M = 0-m-1) where m = _j , I _{2m + j} ... (J = 0 to m-1); in each group G _j , measured fringe image information I _j , I _{m + j} , I
Estimating ideal corrected fringe image information I _j ′ by weighting _{2m + j} (j = 0 to _m −1) according to the amount of phase shift between the actually measured phase point and the reference phase point. And a step of obtaining a phase Φ of the fringe image from the corrected fringe image information I _j ′. The present invention will be described below with reference to the drawings.
FIG. 1 exemplifies a Twyman-Green interferometer as an apparatus to which the fringe image analysis method of the present invention is applied. Light from a semiconductor laser 11 is converted into a parallel light beam via a collimator lens system 12. The light is irradiated on the reference mirror 13. Between the collimator lens system 12 and the reference mirror 13, a half mirror (light beam separating means) 15 is placed, and the light reflected by the half mirror 15 is incident on a surface 16 to be inspected of the object. The optical path length between the half mirror 15 and the reference mirror 13 is set to be longer than the optical path length between the half mirror 15 and the test surface 16 by d. This d is set to, for example, 100 times the reference wavelength λ of the semiconductor laser 11 (when λ = 780 nm, d = 100λ = 78 μm). The light reflected by the reference mirror 13 and the light reflected by the surface 16 to be measured are combined by a half mirror 15 to form an interference fringe via an imaging lens system 17 and a two-dimensional image sensor (a fringe image input means). ) 18 is input. The two-dimensional image sensor 18 has a two-dimensional pixel group. Now, λ = 780 nm, d = 100λ = 7
If it is 8 μm, the reference mirror 13 is 1
Seen at a distance of 00 wavelengths. When the oscillation wavelength of the semiconductor laser 11 increases by 1%, the reference mirror 13 appears 99 wavelengths away, and the reference mirror 13 appears to be
This means that one wavelength is closer to the half mirror 15 side. This is optically equivalent to moving the reference mirror 13 by one wavelength toward the half mirror 15 in a direction perpendicular to the optical axis, and can realize a phase shift without a movable part. [0012] The CPU 21 of the fringe image analysis device 20 has an A /
Receiving the input of the fringe image information from the two-dimensional image sensor 18 that has been A / D converted by the D converter 22,
The current control device (wavelength shift means) 24 is controlled via the D / A converter 23 to control the injection current to the semiconductor laser 11. The CPU 21 is connected to an external storage device 26, a keyboard 27, a display 28, a printer 29, and the like. The above-mentioned known interferometer is formed on the two-dimensional image sensor 18 when the oscillation wavelength of the semiconductor laser 11 is changed by a fraction of the wavelength by the current control device (wavelength shift means) 24. The light intensity at each point of the interference fringes fluctuates in a sinusoidal manner. FIG. 2 shows an example of the state of the change. This change in light intensity is captured by each pixel of the two-dimensional pixel group constituting the two-dimensional image sensor 18, and by observing the change in light intensity, the surface accuracy of the test surface 16 as compared with the reference mirror 13 is measured. Can be detected. In this interferometer, as described above, when the wavelength of the semiconductor laser 11 is changed, not only the wavelength but also the light intensity changes, which results in a phase detection error. The phase detection method of the present invention can accurately detect the phase even when the light intensity changes due to the wavelength change of the semiconductor laser 11 and when there is a shift error in the phase shift amount (wavelength shift amount). That's the way you can. Each step of the method will be described. According to the method of the present invention, first, the phase space of 2π is set to m
Divided into (m ≧ 3) measurement phase points,
4, while shifting the oscillation wavelength of the semiconductor laser 11, a total of n pieces of fringe image information I _{i at} each measurement phase point.
(N ≧ 2m−1) is obtained. FIG. 3 is an example in which the number of divisions (measurement phase points) m of the phase space is selected to be 3, and the number n of fringe image information is selected to be 6, which exactly divides two times in the phase space. In this figure, the measurement result of the first cycle at each measurement phase point is represented by 〇, the measurement result of the second cycle is represented by ●, and these are represented by G ₀ (I ₀ and I ₃ ) and G ₁ (I ₁ and I ₁ ). I ₄ ), G ₂
They are grouped into (I ₂ and I _5). Each group G _i
(That is, the phase difference between the measurement phase points) is preferably equal (120 ° (360 ゜ ÷ 3)), but need not be strictly equal. [0017] The fringe image information I _i of each of these groups G _i
Are not the same due to a change in light intensity due to a change in the wavelength of the semiconductor laser 11 and a phase shift error. The present invention uses the fringe image information I _i of each group G _i, and requests the correct phase in the reference phase point. Now, assuming that the light intensity of the semiconductor laser 11 fluctuates (increases or decreases), in the phase space of FIG.
Each measurement point appears on a spiral curve in which the diameter gradually changes (increases or decreases), and the vertical component of the measurement point is measured as the light intensity (FIG. 4). Here, assuming that the reference phase point is Q and there is no change in light intensity at the reference phase point,
The light intensity is indicated by a broken line in FIGS. The dashed line is shown in FIG.
Is a circle, and in FIG. 4, it is a sine wave curve. However,
Assuming that the light intensity increases, these become a spiral curve and a non-sinusoidal curve whose amplitude gradually increases, respectively, as shown by the solid lines. Taking the measured values I ₀ and I ₃ as an example, they are obtained as I ₀ and I ₃ on a spiral curve and a non-sinusoidal curve. Should be I ₀ '. According to the present invention, in order to estimate this I ₀ ′, a weight corresponding to the amount of phase shift between the actually measured phase point and the reference phase point is assigned to obtain corrected fringe image information I _j ′. From phase Φ
Is what you want. For example, I ₀ ', in FIG. 3, I _0' = - can be estimated with _{[(θ 3 -Δ) I 0} (θ 0 -Δ) I 3] / (θ 3 -θ 0) ····· . Here, Δ is the phase angle of point Q (see FIG. 3)
It is. The value of Δ may be any value, but θ _{0 to} θ _m
Is the optimal value. The same applies to I ₁ ′ and I ₂ ′. Θ ₀ and θ ₃ are originally the same principal values.
In the above example, the reason for setting the angle θ ₃ −θ ₀ = 360 ° (2π) differently is to obtain corrected image information. That is, as shown in FIG. 4, the light intensity I ₀ ^′ at the reference phase point Q can be estimated by expanding θ ₀ and θ ₃ into phase coordinates and capturing variable values different by 360 °. For the estimation, for example, an interpolation method can be used. If the spiral curve makes three or more rounds, I ₀ , I ₃ , I ₆ ... Form a group G _1, which can be estimated using these. When the reference reference point Q matches any of the measurement points, it is not necessary to select a plurality of measurement points for the group of the points. Therefore, the minimum value of the number n of the stripe image information is n = 2m-1, and n ≧ 2m−1 (m ≧ 3) is a condition for n. Next, let us consider a case where the rate of change of the amount of phase shift does not reach the rate assumed in advance with respect to the rate of change of the injection current of the semiconductor laser 11. In this case, FIG. 5, as shown in FIG. 6, the fringe image information I _i is the upper circle or sinusoidal, moves. 5 and 6, the photocurrent does not change,
The period differs between the solid line and the broken line in FIG. From the development in FIG. 5, I ₁ ′ can be estimated from I ₀ (θ ₀ ) and I ₃ (θ ₃ ) as follows. I ₀ ′ = [(θ ₃ −Δ) I ₀ − (θ ₀ −Δ) I ₃ ] / (θ ₃ −θ ₀ ) This equation is the same as the above equation. Therefore, I ₀ ^′ obtained by this equation is simultaneously stable against changes in the intensity and the phase shift amount. The same applies to I ₁ ′ and I ₂ ′. Then, to obtain the phase Φ of the reference phase point from the corrected fringe image information I _i ′ obtained as described above, Φ = tan ⁻¹ (ΣS _i I _i ′ / ΣC _i I _i ′) , S _i , and C _i are values obtained by simultaneously calculating the following equations. ΣC _i = 0 ΣC _i sin θ _i = 0 ΣS _i = 0 ΣS _i cos θ _i = 0 ΣC _i cos θ _i + ΣS _i sin θ _i = 0 (i = 0 to m−1) is a case of dividing the space simply into m, when performing equiangularly this division, C _i and S _i is given by the following equation. In this case, the wavelength shift by the semiconductor laser 11 is given by 2π / m. C _i = cos (2πi / m) S _i = sin (2πi / m) The phase Φ of the fringe image is given by equation (1). [Equation 1] Φ = -tan ^-1 [ΣI _i '· sin (2πi / m)] / [ΣI _i ' · cos
(2πi / m)] (from i = 0 to m−1), the phase Φ of the fringe image is obtained. According to the above method, even if there is a change in the light intensity due to the wavelength shift of the semiconductor laser 11 or a wavelength shift error (phase shift amount error), the correct phase Φ of the fringe image can be obtained. Next, when the 2π phase space is divided into m equal intervals as measurement phase points, a specific algorithm of Φ obtained by applying specific numerical values to m and n Will be described. 1. When m = 3, n = 5, and Δ = 240 °, Φ = tan ⁻¹ [3 ^1/2 (2I ₁ + I ₄ -I ₀ -2I ₃ ) / (6I ₂ -I _0- 2I ₁ -2I ₃ -I ₄ )] When m = 3, n = 6 and Δ = 300 °, [Equation 3] Φ = tan ⁻¹ [3 ^1/2 (5I ₂ + I ₅ -3I ₁ -3I ₄ ) / (2I ₀ -10I ₅ − Three
I ₁ -5I ₂ -3I ₄ -I ₅ )] When the phase is rotated by 120 °, [Equation 4] Φ = tan ^-1 [3 ^1/2 (I ₀ + 5I ₃ -5I ₂ -I ₅ ) / (6I ₁ -6I ₄ -I _0-
5I ₂ -5I ₃ -I ₅ )] When m = 3, n = 9, Δ = 480 ° (linear, 120 ° rotation) [Equation 5] Φ = tan ⁻¹ [3 ^1/2 (I ₀ + 2I ₃ + 3I ₆ -3I ₆ -3I ₂₎ -2I ₅ -I ₈ ) /
(4I ₁ + 4I ₄ + 4I ₇ -I ₀ -3I ₂ -2I ₃ -2I ₅ -3I ₆ -I ₈ )] When m = 4, n = 7 and Δ = 270 °, Φ = tan ⁻¹ [4I ₃ −2I ₁ −2I ₅ ) /
(I ₀ + 3I ₄ -3I ₂ -I ₆ )]. When m = 4, n = 8, and Δ = 315 °, Φ = tan ⁻¹ [7I ₃ + 2I ₇ -3I ₁ -5I ₅ ) /
_{(I 0 + 7I 4 -5I 2} -3I 6)] When delta = 225 DEG, [Formula 8] _{^{Φ = tan -1 [9I 3 -I}} 7 -5I 1 -3I 5) / (3I 0 + 5I 4 - 7I _2-
I ₆ )] [0033] 6. When m = 4, n = 10 and Δ = 405 ° (higher order (second order in G ₀ and G ₁ )), Φ = tan ⁻¹ [80I ₃ + 48I ₇ -7I ₉ -9I ₁ -126I ₅ ) / (126I ₄ +
9I ₈ -7I ₀ -48I ₂ -80I ₆ )] Linear when m = 4, n = 12, Δ = 495 ° [Formula 10] Φ = tan ⁻¹ [25I ₃ + 16I ₇ + 7I ₁₁ -13I ₁ -16I ₅ -19I ₉ )
/ (7I ₀ + 16I ₄ + 25I ₈ -19I ₂ -16I ₆ -13I ₀ )] quadratic [Equation 11] Φ = tan ^-1 [7I ₁ + 33I ₃ + 110I ₇ -126I ₅ -9I ₉ -15
I ₁₁ ) / (110I ₄ + 33I ₈ + 7I ₁₀ -15I ₀ -9I ₂ -126I ₆ )] FIGS. 7 and 8 show a laser light source in a 90 ° system in which the phase space 2π is divided into four. When there is a change in the light intensity and when there is a phase shift deviation, when the correction is made according to the present invention (,), when no correction is made (,), and when the correction is made in the conventional example ( ) Respectively. In the figure, the horizontal axis indicates the phase to be obtained, the left side of the vertical axis indicates the error in units of the number of stripes, and the right side indicates the error in units of phase. The conventional algorithm Φ = tan ^-1 [(I _3-
I ₁ ) / (I ₀ -I ₂ )], and there is no correction effect for both the intensity change and the phase shift deviation. Is a conventional algorithm Φ = tan ⁻¹ [2 (I ₃ −I ₁ ) / (2I ₂ −I ₀ −I ₄ )], and this algorithm has a correction effect on the phase shift deviation, There is no correction effect on the intensity change. Is also a conventional algorithm (linked with the 40th Applied Physics Related Lectures Preliminary Proceedings 31A-ZA-7), and is stable with respect to intensity change, but is more effective with respect to phase shift deviation. Low correction effect. Shows the correction effect of the algorithm according to the present invention based on equation (6). In addition to being stable against a change in intensity, there is an effect equivalent to a phase shift deviation. Shows the correction effect by the algorithm according to the present invention based on Equation 7. In addition to the stability against the intensity change, there is a better correction effect on the phase shift deviation. FIGS. 9 and 10 show that, in the 120 ° system in which the phase space 2π is divided into three, when the light intensity of the laser light source changes and when there is a phase shift deviation, the correction according to the present invention is performed. The case where (,) is added and the case (,) without correction are shown, respectively. The conventional algorithm Φ = tan ^-1 [(I _3-
I ₁ ) / (I ₀ -I ₂ )], and there is no correction effect for both the intensity change and the phase shift deviation. Is the conventional algorithm Φ = tan ^-1 {3 ^1/2 [I ₂ -I ₁ + (I ₃ -I ₀ ) / 3] / (I ₀ -I ₁ -I ₂ +
I ₃ )}, this algorithm has a correction effect on the phase shift deviation, but has no correction effect on the intensity change. Shows the correction effect by the algorithm according to the present invention based on Equation 2. There is a correction effect on the intensity change, and the same effect on the phase shift deviation. Shows the correction effect by the algorithm according to the present invention based on Equation 3. There is a better correction effect on the phase shift deviation while maintaining the correction effect on the intensity change. FIGS. 11 to 13 show the corrected fringe image information I.
_This shows a general method of estimating _i ′. FIG.
This is the case where the value of I _i is two points in the group. In this case, (θ _{j + m} −Δ) vs. (Δ−θ _j ) is set between I _J and I _{j + m.}
Let I 'be the value interpolated in. 12 and 13 show the case where the value of I _i is two or more in the group, FIG. 12 shows the linear estimation, and FIG. 13 shows the higher-order estimation. In FIG. 12, I _j , I _jm , I
A straight line s for fitting _{j + 2m} ... is obtained by least squares approximation, and the value of x = Δ of the straight line is defined as I ′. In FIG.
A curve s ′ connecting I _j , I _jm , I _{j + 2m} ... _Is arithmetically determined, and the value of x = Δ of the curve is I ′. As described above, according to the present invention, in a semiconductor laser phase shift interferometer for controlling an injection current to a semiconductor laser to change its oscillation wavelength, an optical signal is generated along with the change of the oscillation wavelength. Even if the intensity changes and there is a phase shift deviation, the phase can be accurately obtained.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing a configuration of a semiconductor laser phase shift interferometer to which a phase detection method according to the present invention is applied. FIG. 2 is a diagram showing how interference fringes are changed by the apparatus shown in FIG. 1; FIG. 3 is a diagram showing the principle of the present invention when the light intensity changes in the semiconductor laser phase shift interferometer according to the present invention. FIG. 4 is a development view of FIG. 3; FIG. 5 is a diagram showing the principle of the present invention when there is a phase shift error in the semiconductor laser phase shift interferometer according to the present invention. FIG. 6 is a development view of FIG. 5; FIG. 7 shows the detection phase of interference fringes according to the conventional method and the method according to the present invention when the light intensity of the laser light source changes in a 90 ° system in which the phase space 2π is divided into four, and when the light intensity changes. It is a simulation figure of distribution. FIG. 8 is a simulation diagram of a detected phase distribution of interference fringes according to the conventional method and the method of the present invention when the phase shift is shifted and when the phase shift is corrected. FIG. 9 is a diagram illustrating the detection phase of interference fringes according to the conventional method and the method of the present invention when there is a change in the light intensity of the laser light source in a 120 ° system in which the phase space 2π is divided into three, and when this is corrected. It is a simulation figure of distribution. FIG. 10 is a simulation diagram of a detected phase distribution of interference fringes according to the conventional method and the method of the present invention when the phase shift is shifted and when the phase shift is corrected. FIG. 11 is a graph showing an example of an estimation method for estimating correction fringe image information I _i ′. FIG. 12 is a graph showing another example of an estimation method for estimating correction fringe image information I _i ′. FIG. 13 is a graph showing still another example of an estimation method for estimating the corrected fringe image information I _i ′. [Description of Signs] 11 Semiconductor laser 12 Collimator lens system 13 Reference mirror 15 Half mirror 16 Test surface 18 Two-dimensional image sensor (image input means) 20 Stripe image analyzer 21 CPU 24 Current controller (wavelength shift means)

Claims (1)

(57) Claims: 1. An interferometer using a semiconductor laser as a light source, a wavelength shifting means for changing an oscillation wavelength of the semiconductor laser; and inputting fringe image information resulting from the interference. , A fringe image input means having a two-dimensional pixel group, wherein a phase space of 2π is divided into m (m ≧ 3) measurement phase points, While shifting the oscillation wavelength of the semiconductor laser by the shift means, fringe image information is obtained at each measurement phase point, and a total of n pieces of fringe image information I _i (n ≧ 2m−1; m)
≧ 3, i = 0~n-1 , I i is a step of obtaining a light intensity) of each two-dimensional pixel group n pieces of fringe image information; a fringe image information _{I i} of these _{measured, G} j; I _j , I
_{(m + j} , I _{2m + j} ) (j = 0 to m−1); dividing into m groups; In each of the above groups G _j , measured fringe image information I _j ,
I _m + _j, the I 2m + j ··· (j = 0~m-1), denoted by the weight corresponding to the phase shift amount between the reference phase point and the measured phase point, to estimate the correction pattern image information _{I j} ' Determining a phase Φ of the fringe image from the corrected fringe image information I _j ′; and a phase detecting method in the semiconductor laser phase shift interferometer.