JPH10281711A - Method for correcting alignment error - Google Patents

Abstract

PROBLEM TO BE SOLVED: To correct an alignment error accurately and conveniently by fitting information obtained through interference measurement optimally to a surface represented by polar coordinate format. SOLUTION: A polar coordinate system γ, θ, ϕ is represented by a coordinate conversion formula of orthogonal coordinate system x, y, z. When the center of sphere of a surface to be inspected r=R (constant) is located at shix, shiy, shiz with respect to the origin of coordinate 0, 0, 0 at the center of sphere of the measuring wave front of an interferometer, the surface to be inspected can be represented by an expression (x-shix)<2> +(y-shiy)<2> +(z-shiz)<2> =R<2> . The expression is employed along with a coordinate conversion formula for making a conversion into polar coordinate format r=f (R, shix, shiy, shiz; θ, ϕ). Furthermore, the xy coordinate values of interterometer measurement data xi, yi, Δrij obtained for every measurement pixel l, j by each CCD from a variation [dr] of [r] for the shift of alignment represented by a microdisplacement of variables are converted according to the conversion formula into θϕ coordinate values and then the partial differentiation coefficients are calculated for each pixel thus determining the shift.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to an alignment error correction method used for measuring interference of a spherical shape or an aspherical shape.

[0002]

2. Description of the Related Art In general, data obtained by interference measurement is referred to as OPTICAL SHOP TESTING.
426 of (John Wiley and Sons)
Page,

[Number 1] W (xi, yi) = W0 (xi, yi) + A + B · xi + C · yi + D · (xi 2 + yi 2) represented by Formula (1), contains a so-called alignment error I have.

Here, a coefficient A represents a piston error meaning a DC component, a coefficient B represents an X tilt error, a coefficient C represents a Y tilt error, a coefficient D represents a power error, and a system error W0 of the interferometer. (Xi, yi) indicates that it can be deleted by using an appropriate measurement such as Lev subtraction. A calculation method for removing this apparent error is so-called alignment error correction.

[0004]

However, the above equation (1) is only an approximation, and for example, an alignment error (for example, the above-described piston error) can be accurately obtained from the measurement data of the test surface obtained by adding a small aspherical amount to the spherical surface. , Tilt error and power error)
Equation (1) is not sufficient.

An object of the present invention is to provide an alignment error correction method that can easily perform accurate alignment error correction.

[0006]

[Means for Solving the Problems]

(1) The invention according to claim 1 is an alignment error correction for correcting an apparent error caused by misalignment of a test surface included in information of interference fringes obtained by interference measurement of the test surface. Apply to the method. The above-mentioned object is achieved by correcting the error by optimally fitting the information obtained by the interference measurement to the surface represented in the polar coordinate format. (2) The alignment error correction method according to (1), wherein the test surface is a spherical surface or an aspherical surface based on a spherical surface, and the surface to be measured is a spherical surface expressed in a polar coordinate format. This is to perform optimal fitting. (3) The invention according to a third aspect is the alignment error correction method according to the first aspect, wherein the test surface is a secondary aspherical surface,
Alternatively, it is an aspherical surface based on a secondary aspherical surface, and performs optimal fitting for a secondary aspherical surface expressed in a polar coordinate format.

[0007]

BEST MODE FOR CARRYING OUT THE INVENTION

First Embodiment Hereinafter, a first embodiment of an alignment error correction method according to the present invention will be described with reference to FIGS.

A polar coordinate system (r, θ, φ) as shown in FIG.
, The coordinates of the rectangular coordinate system (x, y, z) are

X = r · sin θ · sin φ Equation (2)

Y = r · sin θ · cos φ Equation (3)

## EQU00004 ## z = r.cos .theta. Is represented by the coordinate conversion equation of equation (4).

Now, as the alignment deviation (the cause of the alignment error) when the surface to be measured is spherical, the spherical center of the measurement wavefront (spherical wave) and the surface to be measured (more accurately expressed,
Only the deviation from the spherical center of the optimum approximate spherical surface of the test surface).

[0010] With respect to the coordinate origin (0, 0, 0) located at the spherical center of the measurement wavefront of the interferometer, the spherical center of the surface to be inspected with “r = R (constant value)” is (shix, shiy, shiz ), The test surface is

(X-shix) ² + (y-shiy) ² + (z-shiz) ² = R ² Equation (5)

## EQU1 ## Equation (2)-
Substituting (4) and solving for "r",

R = f (R, shix, shiy, shiz; θ, φ) ... It can be converted into a polar coordinate format as shown in Expression (6).

Further, variables (R, shix, shiy, shiz; θ,
φ), the amount of change “dr” of “r” with respect to misalignment, expressed by the small displacement (dR, dshix, dshiy, dshiz), is

Dr = (７r / ∂R) dR + (∂r / ∂shix) dshix + (∂r / ∂shiy) dshiy + (∂r / ∂shiz) dshiz Approximation by Expression (7) Therefore, x of the interference measurement data (xi, yj, Δrij) obtained for each measurement pixel (i, j) of each CCD can be obtained.
The y coordinate value is

Equation 8 θij = sin ⁻¹ {(xi ² + yj ² ) / R} ^1/2 Equation (8) and

Ijij = tan ⁻¹ (xi / yj) (7) After conversion into the θφ coordinate value using the conversion formula of Expression (9), Expression (7)
Is calculated for each pixel, and the interference measurement data (xi, yj, .DELTA.rij) is optimally fitted by equation (7), whereby the misalignment (dR,
dshix, dshiy, dshiz) can be calculated.

Specifically,

Sum = Σ (Δrij−dr) ² ... With respect to Expression (10),

１１Sum / ∂ (dR) = 0 Equation (11)

１２Sum / ∂ (dshix) = 0 Equation (12)

１３Sum / ∂ (dshiy) = 0 Equation (13)

１４Sum / ∂ (dshiz) = 0 The simultaneous equation of Expression (14) may be solved. Note that a design value may be adopted as “R” in Expression (8).

FIG. 2 shows a simulation result of the alignment error correction method according to the first embodiment. Here, a rectangular aperture is used as the aperture, but the shape of the aperture is not essential.

In the simulation shown in FIG. 2, by giving a known misalignment to an ideal aspherical workpiece in advance with respect to an ideal measurement wavefront, an apparent difference is generated and used instead of the measurement data. . If this data is subjected to optimal approximation fitting by the method described in the first embodiment, the residual yield after the alignment error correction is negligible, and the misalignment can be accurately detected. Is shown. Here, the upper part in each column of FIG. 2A shows the calculation result of the alignment error, the middle part shows the set value of the alignment deviation,
The lower row shows the residual yield, respectively. FIG.
(B) illustrates the residual difference in the rectangular aperture.

-Second Embodiment- As a second embodiment of the alignment error correction method according to the present invention, a method of applying alignment error correction to a secondary aspheric surface is disclosed.

As in the case of the spherical surface, a polar coordinate system (r, θ, φ) as shown in FIG. 1 is considered. At this time, the rectangular coordinate system (X,
Y, Z), the following equations (15) to (17) hold regardless of the spherical surface or the aspherical surface, similarly to the expressions (2) to (4).

X = r · sin θ · sin φ Equation (15)

Y = r · sin θ · cos φ Equation (16)

Z = r · cos θ Expression (17)

The alignment deviation when the secondary aspherical surface is folded back is determined by measuring the spherical center of the spherical wave, which is the measurement wavefront, and the measured secondary aspherical wave defined by the folding mirror, and the actual surface to be measured (more accurately). Is the optimal approximation of the surface to be examined, a secondary aspheric surface)
, The deviation of the first focal point of each surface and the deviation of the secondary aspherical axis itself.

Therefore, the point p on the orthogonal coordinate system (x, y, z) is rotated by “α” around the x axis, and then rotated by “β” around the y axis. With respect to the origin (0,0,0) of the coordinates, the first focal point is set to the design coordinate value (shi
x, shiy, shiz)
The point P on (Y, Z) is represented by the following equation (18).

(Equation 18)

On the other hand,

R = R / {1+ (1-κ) ^1/2 · cos θ} When the secondary aspherical surface expressed in the polar coordinate format of the equation (19) is converted into the orthogonal coordinate system, “r = R (constant value) ”, the following equation (20)
It is represented by

X ² + y ² + z ² = {R− (1−κ) ^1/2 · z} ² (20)

Therefore, equation (18) can be expressed as (x, y, z)
Is substituted into Equation (20), and Equations (15) to (17) are further substituted into Equation (20) to solve for "r".

R = g (κ, R, α, β, shix, shiy, shiz, θ, φ) Expression (21)

Hereinafter, the alignment deviation can be detected by the same method as the spherical surface shown in the first embodiment, and the alignment error can be corrected. However, unlike the case of spherical interference measurement, in the secondary aspherical folded interference measurement, error data in a so-called “oblique incidence” state is measured instead of error data in the normal direction of the surface to be measured. It is necessary to perform so-called "oblique incidence correction" for converting the measurement data into error data in the normal direction of the surface to be measured.

FIG. 3 shows a simulation result of the alignment error correction method according to the second embodiment.
It can be seen that alignment error correction can be performed with high accuracy on the secondary aspheric surface. Here, in each column of FIG. 3A, the upper row shows the calculation result of the alignment shift, the middle row shows the set value of the alignment shift, and the lower row shows the calculation error of the alignment shift. FIG. 3B illustrates the difference in the rectangular aperture, which should be zero, due to the calculation.

Regardless of the spherical surface or the aspherical surface, the alignment error correction formula of the polar coordinate system is generally lower in order than that of the orthogonal coordinate system, and thus has the advantage that the calculation time can be greatly reduced. In the case of a secondary aspherical surface, it is an indispensable technique when measuring the side surface of an elliptical surface. Further, the present invention is also useful for measurement of a test surface on which a minute aspherical amount in a range where interference measurement can be performed based on a spherical surface or an aspherical surface is superimposed.

[0025]

According to the present invention, since the information obtained by the interference measurement is optimally fitted to the surface expressed in the polar coordinate format, the calculation time can be greatly reduced.

[Brief description of the drawings]

FIG. 1 is a diagram showing a polar coordinate system used for an alignment error correction method according to the present invention.

FIGS. 2A and 2B are diagrams illustrating simulation results of the alignment error correction method according to the first embodiment, and FIG. 2A is a diagram illustrating calculation results and the like. (B) is a figure which shows the difference resulting from a calculation.

3A and 3B are diagrams illustrating simulation results of the alignment error correction method according to the first embodiment, and FIG. 3A is a diagram illustrating calculation results and the like. (B) is a figure which shows the difference resulting from a calculation.

Claims (3)

[Claims] 1. An alignment error correction method for correcting an apparent error caused by misalignment of a test surface included in information on interference fringes obtained by interference measurement of a test surface, the method comprising: An alignment error correction method, wherein the error is corrected by optimally fitting information obtained by the interference measurement to the surface represented. 2. The alignment error correction according to claim 1, wherein the test surface is a spherical surface or an aspherical surface based on a spherical surface, and optimal fitting is performed on a spherical surface expressed in a polar coordinate format. Method. 3. The test surface is a secondary aspherical surface or an aspherical surface based on a secondary aspherical surface, and optimal fitting is performed on a secondary aspherical surface expressed in a polar coordinate format. The method for correcting an alignment error according to claim 1.