JP5037432B2 - Wavefront measuring method and apparatus - Google Patents

Description

  The present invention relates to a wavefront measuring method and apparatus.

Conventionally, in order to measure a curved surface shape such as a lens surface, a reflection surface, and a transmission surface of an optical element, or to measure a wavefront aberration of an optical element, an interferometer is used to measure a luminous flux between a measured surface and a reference surface. Various wavefront measurement methods and apparatuses are known in which an interference fringe image is formed by measurement light reflected or transmitted through each of them and a reference light, and the interference fringe image is analyzed to measure the wavefront of the measurement light.
As such a wavefront measurement method, a plurality of interference fringe images are acquired by shifting the phase of the measurement light and the reference light by relatively moving the surface to be measured and the reference surface, and at the same position of each interference fringe image. A fringe scan method is known in which a phase shift amount (phase change) is obtained from a luminance change and a wavefront of measurement light is calculated. For example, an analysis method and an analytical expression for obtaining the wavefront of measurement light using five interference fringe images in which the phase shift amount of each interference fringe image is 0, π / 2, π, 3π / 2, and 2π are 5 This is known as the bucket method. In addition, a 7-bucket method, a 9-bucket method, a 13-bucket method, and the like are known depending on the number of interference fringe images used for analysis.
For example, in Patent Document 1, a test lens is held movably in the optical axis direction by a coarse motion mechanism using a micrometer head and a fine motion mechanism composed of a piezoelectric element, and the test lens is tested against the reference lens. The lens is moved by λ / 8 (λ is the wavelength of the light source) corresponding to the phase shift amount of π / 2, and the interference fringe image is picked up by the interference fringe image pickup unit at each moving position. An interferometer (wavefront measuring apparatus) is described in which interference fringe image data is taken into an interference fringe analyzer five times and a wavefront can be obtained from the obtained five interference fringe images by a five-bucket method. .
According to the interferometer described in Patent Document 1, first, the lens to be tested is positioned at a position where an interference fringe image can be obtained by a coarse movement mechanism, and five interference fringe images are obtained and the wave front is obtained by the 5-bucket method. , And using this wavefront information and lens data of the lens to be tested, the amount of positional deviation in the optical axis direction of the lens to be tested from the position where the measurement error of the wavefront is minimized. Then, the fine movement mechanism is driven based on the positional deviation amount, and the wavefront and the positional deviation amount are similarly obtained, and this is repeated until the positional deviation amount falls within the allowable range. The surface shape of the lens surface is calculated from the wavefront.
JP 2005-265586 A

However, the conventional wavefront measuring method and apparatus as described above have the following problems.
In the technique described in Patent Document 1, the wavefront is calculated by the fringe scan method, and the amount of positional deviation in the optical axis direction of the test lens with respect to the reference lens from the position where the measurement error of the wavefront is minimized, Since this misalignment is corrected, the measurement accuracy of wavefront measurement can be improved as compared with the case where the misalignment is not corrected. However, the piezoelectric element used as the fine movement mechanism has nonlinear characteristics and hysteresis characteristics, and aligns the distance between the reference lens and the test lens in the optical axis direction with a positioning accuracy of tens of nanometers or less. It ’s difficult. Therefore, there is a problem that the wavefront measurement cannot be performed with higher accuracy than the positioning accuracy of the piezoelectric element.

  The present invention has been made in view of the above problems, and can reduce the measurement error due to the positioning accuracy of the relative movement of the measured surface and the reference surface, and improve the measurement accuracy of wavefront measurement. An object is to provide a measurement method and apparatus.

In order to solve the above-described problem, in the invention described in claim 1, the same light beam is divided into measurement light reflected or transmitted by a measurement surface that is a curved surface and reference light that interferes with the measurement light. Then, a wavefront of either the reference light or the measurement light is converted by a curved reference surface, and interference fringes are formed by the measurement light and the reference light, and the measured surface and the reference surface are Acquiring n interference fringe images (n is an integer of 3 or more) that can be regarded as having a certain phase increment by relatively moving in the optical axis direction, and using the n interference fringe images, the measurement is performed. A wavefront measuring method for measuring a wavefront of light, wherein the relative position of the surface to be measured and the reference surface in the optical axis direction includes a measurement reference position in the optical axis direction that minimizes the number of interference fringes. The phase difference between the measurement light and the reference light is constant. Candidates for obtaining the information on the relative position and m candidate images (m is an integer greater than n) that are candidates for the n interference fringe images by moving so as to change at a pitch finer than the phase increment. From the image acquisition step and the m candidate images acquired in the candidate image acquisition step, the analysis candidate image group for calculating the wavefront of the measurement light is regarded as having the constant phase increment. An analysis candidate image group selection step of selecting a plurality of sets of n candidate images capable of being analyzed, and analyzing each of the sets by analyzing each of the plurality of analysis candidate image groups selected in the analysis candidate image group selection step A wavefront calculation step for calculating a wavefront according to the candidate image group, and a position in the optical axis direction from the measurement reference position of the acquisition position of each analysis candidate image group from the information on each wavefront calculated in the wavefront calculation step Evaluate the amount of deviation and A wavefront evaluation value of the shift amount is minimized, and a method and a wavefront selection step of selecting as the wavefront of the measuring light.
According to the present invention, in the candidate image acquisition step, the phase difference between the measurement light and the reference light is finer than the constant phase increment within a range including the measurement reference position in the optical axis direction in which the number of interference fringes is minimized. M candidate images that are candidates for n interference fringe images are acquired by moving the image to change with the pitch, and an analysis candidate image group is selected from the m candidate images in the analysis candidate image group selection step. A plurality of sets of n candidate images that can be regarded as having a certain phase increment, a wavefront according to each set of analysis candidate images in the wavefront calculation step is calculated, and in the wavefront selection step, From the calculated wavefront information, the positional deviation amount from the measurement reference position in the optical axis direction of the acquisition position of each analysis candidate image group is evaluated, and the wavefront having the smallest evaluation value of the positional deviation amount is determined as the measurement light. Select as wavefront.
In this way, even if the positioning accuracy is low when moving the relative position of the measured surface and the reference surface in the optical axis direction, within the range of accuracy of the moving feed amount that is higher than the positioning accuracy. From the m candidate images, the candidate image closest to the measurement reference position and the n analysis candidate image groups having a certain phase increment around the candidate image can be selected, so that the wavefront measurement can be performed with high accuracy. It can be carried out.

According to a second aspect of the present invention, in the wavefront measuring method according to the first aspect, in the wavefront selection step, the wavefronts calculated in the wavefront calculation step are approximated by a quadratic equation expressed by the following equation. In this case, the positional deviation amount is evaluated from the magnitude of the coefficient of the quadratic term of the quadratic expression.
Z (X, Y) = C ₀ + C ₁ · X + C ₂ · Y + C ₃ · (X ² + Y ² ) (1)
Here, (X, Y, Z) is the coordinate value of the wave front in the XYZ rectangular coordinate system in which the optical axis direction is the Z-axis direction, C ₀ is a constant term, C ₁ and C ₂ are primary terms, and C 3 is It is an approximation coefficient of a quadratic term.
According to the invention, it possible to evaluate the positional deviation amount from the relationship between the power components of the wavefront represented by the coefficients C ₃ of the second-order terms of the positional deviation amount and the formula (1) from the measurement reference position in the optical axis direction it can.

According to a third aspect of the present invention, in the wavefront measurement method according to the first or second aspect, in the candidate image acquisition step, the relative position in the optical axis direction is changed in one direction while a constant sampling period is set. The time-series candidate images are acquired, and the relative position information is acquired as position information on the time series. In the analysis candidate image group selection step, it can be regarded as having the constant phase increment. A plurality of candidate images are selected by performing an operation of estimating a relationship between position information on the time series and a phase from a luminance change of interference fringes at a fixed position of the time series candidate images.
According to the present invention, in the candidate image acquisition step, the time-series candidate images are acquired at a constant sampling period while changing the relative position in the optical axis direction in one direction, and in the analysis candidate image group selection step, A plurality of candidate images that can be considered to have a certain phase increment are calculated by estimating the relationship between the position information on the time series and the phase from the luminance change of the interference fringes at a certain position of the candidate images in the time series. Therefore, even if a moving mechanism having a non-linear characteristic or a hysteresis characteristic such as a piezoelectric element is used, control becomes easy and accurate measurement can be performed.

According to a fourth aspect of the present invention, in the wavefront measurement method according to the first or second aspect, in the candidate image acquisition step, the relative position in the optical axis direction is measured while changing the relative position in the optical axis direction. Thus, the information on the relative position and the candidate image are acquired, and in the analysis candidate image group selection step, a plurality of candidate images that can be regarded as having the constant phase increment are obtained by using the measured relative position. The method is based on information.
According to this invention, in the candidate image acquisition step, by measuring the relative position in the optical axis direction while changing the relative position in the optical axis direction, information on the relative position and the candidate image are acquired, and the analysis candidate image group In the selection process, a plurality of candidate images that can be regarded as having a certain phase increment are selected based on the information of the measured relative positions. For example, a moving mechanism having nonlinear characteristics such as a piezoelectric element is used. However, accurate measurement can be performed without taking time and effort such as calibration of the movement amount.

The invention according to claim 5 is the wavefront measurement method according to any one of claims 1 to 4, wherein the constant phase increment is π / 2 and n is 5.
According to the present invention, since five interference fringe images that can be regarded as being shifted in phase by π / 2 are used, highly accurate and quick measurement can be performed.

In the invention according to claim 6, the same light beam is divided into measurement light reflected or transmitted by a measurement surface made of a curved surface and reference light made to interfere with the measurement light, and the reference surface made of a curved surface is used to The wavefront of either the reference light or the measurement light is converted to form interference fringes by the measurement light and the reference light, and n (n is 3 or more) that can be regarded as having a certain phase increment A wavefront measuring apparatus for measuring a wavefront of measurement light using the n interference fringe images acquired by the interferometer, the interferometer acquiring an integer) interference fringe image, And the relative position in the optical axis direction of the reference surface is within a range including the measurement reference position in the optical axis direction in which the number of fringes of the interference fringes is minimum, the phase difference between the measurement light and the reference light is the constant Move to change at finer pitch than phase increment A relative movement mechanism, a relative position information acquisition unit that acquires information of the relative position from the relative movement mechanism, and m pieces of m interference fringe image candidates from the interferometer (m is from n) A candidate image acquisition unit that acquires (large integer) candidate images, and a memory that stores the relative position information acquired by the relative position information acquisition unit and the candidate image acquisition unit and the m candidate images in association with each other. A fixed phase increment as an analysis candidate image group for calculating the wavefront of the measurement light from the relative position information and the m candidate images stored in the storage unit An analysis candidate image group selection unit that selects a plurality of sets of n candidate images that can be considered, and the plurality of analysis candidate image groups selected by the analysis candidate image group selection unit, respectively, Solution of A wavefront calculation unit that calculates a wavefront according to the candidate image group, and the position in the optical axis direction from the measurement reference position of the acquisition position of each analysis candidate image group from the information of each wavefront calculated by the wavefront calculation unit A wavefront selecting unit that evaluates the deviation amount and selects a wavefront that minimizes the evaluation value of the positional deviation amount as the wavefront of the measurement light is provided.
According to the present invention, the phase difference between the measurement light and the reference light is more than a constant phase increment within a range including the measurement reference position in the optical axis direction in which the number of interference fringes is minimized by the relative movement mechanism and the interferometer Interference fringes are generated while changing at a fine pitch, m candidate images that are candidates for n interference fringe images are obtained by the candidate image obtaining unit, and the surface to be measured and the reference surface are obtained by the relative position information obtaining unit. The relative position information in the optical axis direction is acquired, and the acquired relative position information and m candidate images are stored in the storage unit in association with each other. Then, the analysis candidate image group selection unit can determine that the analysis candidate image group has a certain phase increment from the relative position information and the m candidate images stored in the storage unit. A plurality of sets of candidate images are selected, and the wavefront calculation unit calculates a wavefront corresponding to each set of analysis candidate images. Then, the wavefront selection unit evaluates the positional deviation amount from the measurement reference position in the optical axis direction of the acquisition position of each analysis candidate image group from the calculated wavefront information, and the evaluation value of this positional deviation amount is the minimum. Is selected as the wavefront of the measurement light.
Thus, when moving the relative position of the measured surface and the reference surface in the optical axis direction, even if the positioning accuracy of the relative movement mechanism is low, the accuracy of the moving feed amount is higher than the positioning accuracy. In this range, it is possible to select a candidate image closest to the measurement reference position and n analysis candidate image groups having a constant phase increment around the candidate image from among the m candidate images. Wavefront measurements can be made.
A wavefront measuring apparatus according to a sixth aspect is an apparatus that can be used in the wavefront measuring method according to the first aspect.

According to a seventh aspect of the present invention, in the wavefront measuring apparatus according to the sixth aspect, the wavefront selecting unit approximates each wavefront calculated by the wavefront calculating unit with a quadratic expression expressed by the following expression. The positional deviation amount is evaluated from the magnitude of the coefficient of the quadratic term of the quadratic expression.
Z (X, Y) = C ₀ + C ₁ · X + C ₂ · Y + C ₃ · (X ² + Y ² ) (1)
Here, (X, Y, Z) is the coordinate value of the wavefront in the XYZ rectangular coordinate system in which the optical axis direction is the Z-axis direction, C ₀ is a constant term, C ₁ and C ₂ are primary terms, and C ₃ Is an approximation coefficient of a quadratic term.
According to the invention, it possible to evaluate the positional deviation amount from the relationship between the power components of the wavefront represented by the coefficients C ₃ of the second-order terms of the positional deviation amount and the formula (1) from the measurement reference position in the optical axis direction it can.

  According to the wavefront measuring method and apparatus of the present invention, a plurality of sets of analysis candidate images are selected from m candidate images, each wavefront is calculated, and the optical axis from the measurement reference position is determined based on the information on each wavefront. Since the wavefront that minimizes the evaluation value of the amount of displacement in the direction is obtained, the measurement error due to the positioning accuracy of the relative movement of the measurement surface and the reference surface can be reduced, and the measurement accuracy of wavefront measurement can be improved. Play.

  Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. In all the drawings, even if the embodiments are different, the same or corresponding members are denoted by the same reference numerals, and common description is omitted.

[First Embodiment]
A wavefront measuring apparatus according to a first embodiment of the present invention will be described.
FIG. 1 is a schematic configuration diagram showing a schematic configuration of the wavefront measuring apparatus according to the first embodiment of the present invention. FIG. 2 is a functional block diagram showing a functional configuration of control means of the wavefront measuring apparatus according to the first embodiment of the present invention.

The wavefront measuring apparatus 50 according to the present embodiment can measure the wavefront of the reflected light on the surface to be measured 5 using an interferometer 51 having a Fizeau optical system, and can measure the surface shape of the surface to be measured 5. Is. The wavefront measuring apparatus 50 is an apparatus that can implement the wavefront measuring method according to the first embodiment of the present invention.
As shown in FIG. 1, the schematic configuration of the wavefront measuring apparatus 50 includes a laser light source 1, a collimating lens 2, a beam splitter 3, a Fizeau lens 4, a piezo element 8 (relative movement mechanism), a piezo element controller 9, and an adjustment stage 12. , A condenser lens 6, a CCD 7, and a measurement control unit 10. In order to perform operation input and setting information input necessary for shape measurement, the measurement control unit 10 displays, for example, an operation unit 13 including a keyboard, a mouse, and the like, an image captured by the CCD 7, a shape measurement result, and the like. Therefore, the display unit 11 including a monitor or the like is electrically connected.
Here, the laser light source 1, the collimator lens 2, the beam splitter 3, the Fizeau lens 4, and the condenser lens 6 constitute an interferometer 51.
Although an appropriate shape can be measured as the surface 5 to be measured, a description will be given below using a configuration example in the case of measuring the concave shape.

The laser light source 1 is a light source that generates coherent light for forming interference fringes. In this embodiment, as an example, a light source that generates laser light having a wavelength λ = 632.8 (nm) as divergent light is employed. ing.
The divergent light generated by the laser light source 1 is converted into parallel light 30 a (the same light beam) by the collimator lens 2 and is incident on the beam splitter 3.
The beam splitter 3 reflects and guides the parallel light 30a onto the optical axis of the Fizeau lens 4, and transmits a measurement surface reflected light 30c and a reference surface reflected light 30d, which will be described later, incident from the Fizeau lens 4 side. It is.

The Fizeau lens 4 reflects a part of the parallel light 30a incident on the optical axis by the Fizeau surface 4a (a reference surface made of a curved surface) to form a reference surface reflected light 30d (reference light). Is a lens that transmits the other part of the parallel light 30a incident thereon as transmitted light 30b and condenses the transmitted light 30b.
The shape of the Fizeau surface 4a is finished with high accuracy in accordance with the ideal shape of the surface 5 to be measured. Therefore, the Fizeau surface 4a constitutes a reference surface for converting the wavefront of the measurement surface reflected light 30c reflected by the measurement surface 5 to form an interference fringe with the reference surface reflected light 30d.

The piezo element 8 holds the Fizeau lens 4 so as to be movable in the direction along the optical axis, and moves relative to the measurement surface 5 whose position is fixed by the adjustment stage 12 to change the relative position of the Fizeau surface 4a in the optical axis direction. Mechanism. Thereby, the optical path difference between the measured surface reflected light 30c and the reference surface reflected light 30d on the Fizeau surface 4a can be changed by a minute amount that is sufficiently smaller than the wavelength λ.
The movable range of the piezo element 8 may be λ / 2 or more. However, in order to simplify the position adjustment before the measurement is started by the adjustment stage 12, it is preferably as wide as possible. For example, it is preferable that the movement of about 2λ or 3λ (or 1.2 μm to 1.9 μm) is possible.
The amount of movement of the piezo element 8 is controlled by changing the applied voltage by a piezo element controller 9 electrically connected to the piezo element 8.

The piezo element controller 9 controls the voltage applied to the piezo element 8 based on a control signal from the measurement control unit 10 and controls the amount of expansion / contraction of the piezo element 8, thereby the Fizeau surface 4 a with respect to the measured surface 5. The relative position in the optical axis direction is controlled.
As shown in FIG. 2, the schematic configuration of the piezo element controller 9 includes a calculation unit 35, a timer 36, a D / A conversion unit 37, and an amplifier unit 38.
The calculation unit 35 generates applied voltage data that linearly increases the applied voltage from 0 V to the command voltage within the rise time in accordance with the rise time and command voltage control signal sent from the measurement control unit 10, and performs measurement. The applied voltage data is sequentially supplied to the D / A converter 37 in accordance with a movement start signal from the controller 10.
The timer 36 supplies a reference clock for sending applied voltage data from the calculation unit 35 to the amplifier unit 38 at an appropriate cycle.
The D / A converter 37 converts the applied voltage data supplied by the calculator 35 into a voltage signal. This voltage signal is amplified by the amplifier unit 38 and output to the piezo element 8 as an applied voltage for driving the piezo element 8.
Thus, according to the piezo element controller 9 of the present embodiment, an applied voltage for continuously driving the piezo element 8 in a certain direction can be supplied in accordance with the movement start signal from the measurement control unit 10. It has become.

The adjustment stage 12 aligns the optical axis of the surface 5 to be measured with the optical axis of the interferometer 51, and initially sets the distance in the optical axis direction with respect to the Fizeau surface 4a. In this embodiment, for example, the interferometer The XYZ stage that adjusts the relative position in the direction of the optical axis 51 and the direction orthogonal to the optical axis, and the biaxial gonio stage that adjusts the tilt angle of the interferometer 51 with respect to the optical axis.
The surface to be measured 5 supported by the adjustment stage 12 has at least the surface shape to be measured so that the optical axis of the surface to be measured 5 coincides with the optical axis of the Fizeau lens 4 and the curvature of the surface to be measured 5. The center is arranged so as to be located in the vicinity of the condensing position of the transmitted light 30b by the Fizeau lens 4.
Hereinafter, the fact that the position in the optical axis direction of the center of curvature of the measurement surface 5 coincides with the position where the transmitted light 30b is collected by the Fizeau lens 4 is referred to as the measurement reference position. At the measurement reference position, the number of interference fringes described later is minimized.

The transmitted light 30b incident on the measured surface 5 is reflected as the measured surface reflected light 30c. At this time, since the optical axes of the measured surface 5 and the Fizeau lens 4 coincide and the center of curvature of the measured surface 5 is located in the vicinity of the condensing position of the Fizeau lens 4, the light beam of the transmitted light 30b is reflected. Incident along the normal line of the measurement surface 5, the measured surface reflected light 30 c travels back in substantially the same optical path as the transmitted light 30 b, reenters the Fizeau lens 4, and the reference surface reflected light on the Fizeau surface 4 a. An interference fringe is formed with 30 d and transmitted toward the beam splitter 3.
Therefore, both the measured surface reflected light 30c and the reference surface reflected light 30d are formed by dividing the parallel light 30a that is the same light beam (that is, originally the same one light beam) by the Fizeau surface 4a. Luminous flux. Then, the measured surface reflected light 30 c is reflected by the measured surface 5 to be measured light whose wavefront has changed according to the shape of the measured surface 5. On the other hand, the reference surface reflected light 30d is reflected by the Fizeau surface 4a, thereby becoming reference light having a wavefront corresponding to the shape of the Fizeau surface 4a. Further, the measured surface reflected light 30c is reflected by the measured surface 5 and travels backward in substantially the same optical path, so that the optical path between the Fizeau surface 4a and the measured surface 5 with respect to the reference surface reflected light 30d. The optical path difference is approximately twice the length.

The condenser lens 6 is an optical element that projects interference fringes due to the measurement surface reflected light 30 c and the reference surface reflected light 30 d onto the imaging surface 7 a of the CCD 7.
The CCD 7 is an image sensor that photoelectrically converts an interference fringe image projected on the imaging surface 7a at a predetermined video rate. As the video rate, an appropriate value can be adopted as necessary. For example, a video rate of 30 fps can be preferably adopted.
The CCD 7 is electrically connected to the measurement control unit 10, the imaging operation is controlled by the measurement control unit 10, and the image signal captured by the CCD 7 is sent to the measurement control unit 10.

  As shown in FIG. 2, the functional block configuration of the measurement control unit 10 includes an image acquisition unit 20, a candidate image acquisition unit 21, a movement control unit 22, a storage unit 23, an analysis candidate image group selection unit 24, a wavefront calculation unit 25, It comprises a wavefront selection unit 26 and a display control unit 27.

  The image acquisition unit 20 captures the image signal sent from the CCD 7 for each image frame at the timing instructed by the candidate image acquisition unit 21, converts it into luminance data, and converts the image data into two-dimensional image data. To send to.

The candidate image acquisition unit 21 controls the timing of image capture of the image acquisition unit 20 based on the operation input of the operation unit 13, and based on the information of the movement start position and the movement end position set in advance from the operation unit 13. The conditions of the movement operation of the movement control unit 22 are set, and a movement start signal is transmitted based on the operation input of the operation unit 13.
Then, when the image acquisition by the image acquisition unit 20 is started, the candidate image acquisition unit 21 sequentially includes phase changes in time series corresponding to the movement of the Fizeau surface 4a from the image acquisition unit 20 in a certain direction. The image data (hereinafter referred to as time-series images) transmitted to the storage unit 23 is associated with the information on the order of capture (hereinafter referred to as time-series position information) corresponding to the phase at each moving position in the storage unit 23. Remember. For example, when the i-th time series image acquired on the time series is F _i (where i = 1,..., M), the candidate image acquisition unit 21 determines the time-series image according to the value of i. which is to call the F _i.
Here, i is position information on the time series, and the time series image F _i corresponding to _i forms a candidate image that is a candidate of n interference fringe images that can be regarded as having a certain phase increment. ing.
In this embodiment, the candidate image acquisition unit 21 sets m for the movement control unit 22 in the movement range L in the optical axis direction including the measurement reference position (where m is an integer of 4 or more). In order to obtain the candidate image, a condition is set such that the command voltage to the piezo element 8 is changed at a constant speed within a certain rise time T. For this reason, the sampling period ΔT of the candidate image acquisition unit 21 is ΔT = T / (m−1).

  As described above, the candidate image acquisition unit 21 according to the present embodiment sets the conditions for the movement operation of the piezo element 8 so that the time-series position information i is obtained in the optical axis directions of the measured surface 5 and the Fizeau surface 4a The relative position information is used. Therefore, the candidate image acquisition unit 21 also serves as a relative position information acquisition unit that acquires relative position information from the piezo element 8 (relative movement mechanism).

The movement control unit 22 controls the piezo element controller 9 based on the set value of the movement operation condition and the movement start signal from the candidate image acquisition unit 21, and the movement of the piezo element 8 by the control of the piezo element controller 9 is completed. When this is detected, the candidate image acquisition unit 21 is notified, and thereafter, the piezo element 8 is controlled to return to the initial state.
Thus, in the present embodiment, the Fizeau lens 4 is moved by the distance L by the piezo element 8 being continuously extended in a certain direction within a certain time T.
The storage unit 23 stores the time-series image F _i sent from the candidate image acquisition unit 21 and the position information i on the time series.

The analysis candidate image group selection unit 24 calculates the shape of the measurement target surface 5 from the time-series position information i stored in the storage unit 23 and the m time-series images F _i corresponding to _i. As the analysis candidate image group, a plurality of sets of n analysis candidate image groups (where n is an integer of 3 ≦ n <m) that can be regarded as having a certain phase increment Δφ are selected. . For example, the k th analysis candidate image group G _k is represented by G _k = {F _k , F _k1 ,..., F _{k (n−1)} } (where each subscript has a size of 1 to m, The order of the sizes is expressed as k <k1 <... <K (n−1)).
In the present embodiment, an example of Δφ = π / 2 and n = 5 will be described as an example. This Δφ = π / 2 corresponds to λ / 8 as the moving distance of the Fizeau lens 4. The number m of image data is selected so that an error with respect to Δφ of the phase difference between n candidate images is sufficiently small. In the present embodiment, a case where m = 40 will be described as an example.

The wavefront calculation unit 25 calculates the wavefront h _k of each time-series image from the analysis candidate image group G _k selected by the analysis candidate image group selection unit 24. In this embodiment, as an example, P. Hariharan, BF Oreb (BFOreb), T. Eiju, "Applied Optics", (USA) 1987, 26, pp. 2504-2506, which is calculated from the so-called 5-bucket method.
For example, from the analysis candidate image group G _k , the luminance at each of the time-series images F _k , F _k1 , F _k2 , F _k3 , and F _{k4 at} a fixed position (represented by coordinates (x, y)) is respectively position intensity data. When expressed as g _j (x, y) (where j = 1,..., 5), the phase θ _k (x, y) at the coordinates (x, y) can be calculated from the following equation (2). . However, in Equation (2), for simplicity, θ _k (x, y) and g _j (x, y) are represented by θ and g _j , respectively.
Here, the coordinates (x, y) mean coordinates in the xy coordinate system in which the optical axis position is the origin (0, 0) in a plane orthogonal to the optical axis. Since the xy coordinate system is associated with the position on the interference fringe image by the projection magnification of the condenser lens 6 in the measurement control unit 10, the position on the image is simply ( x, y).

That is, the wavefront h _k (x, y) of each time-series image calculated from the analysis candidate image group G _k is expressed by the following equation (2) using the phase θ _k (x, y) represented by the equation (2): 3). In the following, when there is no possibility of misunderstanding, (x, y) may be omitted and simply referred to as wavefront h _k and phase θ _k .

h _k (x, y) = λ · θ _k (x, y) / 4π (3)

Wavefront selector 26, the information of each wavefront h _k, to evaluate positional deviation amount ΔZ from the measurement reference position in the optical axis direction acquiring position for each time series image analysis candidates image group G _k, the positional deviation amount The wavefront h _k that minimizes the evaluation value of ΔZ is selected as the wavefront h that represents the shape of the measured surface 5.
ΔZ of the present embodiment is calculated from the following equation (4) using a coefficient C ₃ that is a power component when the wavefront h _k is approximated by the following equation (1).

Z (X, Y) = C ₀ + C ₁ · X + C ₂ · Y + C ₃ · (X ² + Y ² ) (1)
Here, (X, Y, Z) is the coordinate value of the wavefront in the XYZ rectangular coordinate system in which the optical axis direction is the Z-axis direction, C ₀ is a constant term, C ₁ and C ₂ are primary terms, and C ₃ Is an approximation coefficient of a quadratic term.

Here, F _no is the F number of the measured surface 5. Equation (4) gives a good evaluation value for ΔZ when the radius of curvature of the surface to be measured 5 is sufficiently larger than ΔZ.

  The display control unit 27 converts the image data sent from the image acquisition unit 20 into, for example, an NTSC signal and sends it to the display unit 11 to display an interference fringe image on the display unit 11 or the wavefront selection unit 26. The image information and the character information of the measurement result such as the wavefront h selected by (1) are displayed on the display unit 11.

  The apparatus configuration of the measurement control unit 10 may be realized by using the dedicated hardware for each of the above functions. In this embodiment, the apparatus is configured by a computer including a CPU, a memory, an input / output interface, an external storage device, and the like. These functions are realized by executing appropriate control programs by this computer.

Next, the operation of the wavefront measuring apparatus 50 will be described focusing on the wavefront measuring method of the present embodiment.
FIG. 3 is a flowchart showing a measurement flow of the wavefront measuring method according to the first embodiment of the present invention. FIG. 4 is a flowchart for explaining the operation of the candidate image acquisition step of the wavefront measuring method according to the first embodiment of the present invention. FIG. 5 is a schematic diagram of candidate images acquired in the candidate image acquisition step of the wavefront measurement method according to the first embodiment of the present invention. FIG. 6 is a schematic graph showing an example of an approximate curve in the candidate image acquisition step of the wavefront measuring method according to the first embodiment of the present invention. Here, the horizontal axis represents time, and the vertical axis represents luminance. FIGS. 7A and 7B are diagrams for explaining an example of an analysis candidate image group and another example selection method in the analysis candidate image group selection step of the wavefront measurement method according to the first embodiment of the present invention, respectively. It is a typical graph. Here, the horizontal axis indicates time-series position information i, and the vertical axis indicates the phase change amount p (i). 8A, 8B, 8C, 8D, and 8E show examples of wavefronts calculated for each analysis candidate image group and displayed on the display unit. FIG. 9 is a schematic diagram for explaining the positional deviation amount ΔZ in the optical axis direction.

In the Fizeau-type optical system used in the wavefront measuring apparatus 50, as shown in FIG. 1, when the laser light source 1 is oscillated, divergent light of wavelength λ is generated, and collimated lens 2 forms parallel light 30a. And is incident on the optical axis of the Fizeau lens 4.
The parallel light 30a is divided by the Fizeau surface 4a, and a part thereof is reflected by the Fizeau surface 4a toward the beam splitter 3 and proceeds as reference surface reflected light 30d. Other light is transmitted as transmitted light 30 b, condensed by the lens action of the Fizeau lens 4, condensed at one point, then guided to the measurement surface 5 and incident in the normal direction of the measurement surface 5. By doing so, it is reflected as the measured surface reflected light 30c. The measured surface reflected light 30c travels backward along the same optical path as the transmitted light 30b, passes through the Fizeau lens 4, and is emitted to the beam splitter 3 side. At that time, an interference fringe image corresponding to the optical path difference between the measured surface reflected light 30c and the reference surface reflected light 30d is formed on the Fizeau surface 4a.
This interference fringe image is projected onto the imaging surface 7 a of the CCD 7 by the condenser lens 6. The interference fringe image is photoelectrically converted by the CCD 7 and sent to the measurement control unit 10 as an image signal, and displayed on the display unit 11 via the display control unit 27.

  First, the measurer drives the adjustment stage 12 while viewing the interference fringe image shown on the display unit 11, and sets the position of the surface to be measured 5 in the direction perpendicular to the optical axis of the interferometer 51 and the tilt angle with respect to the optical axis. adjust. And it moves to an optical axis direction, the range from which an interference fringe image is acquired is confirmed, and a measurement start position is set.

By this initial adjustment, when the Fizeau lens 4 and the measured surface 5 are positioned at the measurement reference position, interference fringes due to only the shape error between the Fizeau surface 4a and the measured surface 5 are observed. On the other hand, when the position of the Fizeau lens 4 in the optical axis direction is deviated from the measurement reference position by the positional deviation amount ΔZ, an optical path difference due to the positional deviation occurs. In addition to the shape error, a measurement error derived from the positional deviation amount ΔZ is superimposed on the wavefront.
For example, in order to measure the surface shape of a lens having an F number of 0.6 with an accuracy of 0.01 λ or less, it is necessary to adjust the positional deviation amount ΔZ to 14 nm or less. It was extremely difficult to obtain a high positioning accuracy.

In the wavefront measuring method of the present embodiment, an interference fringe image is obtained by changing the position in the optical axis direction between the Fizeau surface 4a and the measured surface 5 within a range including the measurement reference position, and the calculation result of the wavefront is obtained. Then, the positional deviation amount ΔZ is evaluated, and the calculation result of the wavefront that minimizes | ΔZ | is selected as the wavefront that represents the surface shape of the measured surface 5.
Therefore, a candidate image acquisition process, an analysis candidate image group selection process, a wavefront calculation process, and a wavefront selection process are sequentially performed along the measurement flow shown in FIG.

In the candidate image acquisition step, the measured surface reflected light is measured within the range in which the measurement reference position in the optical axis direction where the number of interference fringes is minimized is included in the relative positions of the measurement surface 5 and the Fizeau surface 4a in the optical axis direction. This is a step of acquiring position information i on the time series and m time series images F _i by moving the phase difference between 30c and the reference surface reflected light 30d so as to change at a pitch finer than Δφ.
This process corresponds to step S1 in the measurement flow of FIG.

Step S1 is realized by the flow shown in FIG. 4, and the Fizeau lens 4 is continuously moved in a fixed direction by a distance L during a rising time T set in advance by the piezo element 8 and set in advance. M interference fringe images are sequentially acquired at every sampling period ΔT, and time series images F ₁ , F ₂ ,..., F are stored in the storage unit 23 together with time series position information i representing the acquisition order. _m (see FIG. 5).
In the present embodiment, as an example, a case where L = 1.3λ / 2 and T = 1.3 (s) will be described. The sampling period ΔT is set to ΔT = 1/30 (s) in accordance with the video rate 30 fps of the CCD 7 of the present embodiment. That is, in this example, each frame image during the time T is captured and a time-series image with m = 40 is acquired.

First, as shown in FIG. 4, in step S11, a command voltage (controller operation command) that causes the movement control unit 22 to expand or contract the piezo element 8 by L at the rising time T from the operation unit 35 of the piezo element controller 9 is shown. ) And then a movement start signal 100 is sent. Then, on the measurement control unit 10 side, the process proceeds to step S12.
On the piezo element controller 9 side, when information on the rise time T and the command voltage is received from the movement control unit 22, step S20 is executed.
In step S20, the calculation unit 35 performs setting so that applied voltage data proportional to time is output from 0 V to the command voltage within the rising time T. When the movement start signal is received, the timer 36 is initialized and step S21 is executed.
In step S 21, the applied voltage data is converted into a voltage signal by the D / A converter 37 according to the value of the timer 36, amplified appropriately by the amplifier 38, and applied to the piezo element 8.
In step S22, it is determined whether or not the value of the timer 36 has exceeded the rising time T. If the rising time T has not been exceeded, the process proceeds to step S21.
When the rise time T is exceeded, the movement control unit 22 is notified of the movement end by sending the movement end signal 101, the voltage output is stopped, and the position of the piezo element 8 is returned to the initial state.

In step S12, the candidate image acquisition unit 21 acquires an interference fringe image from the CCD 7 in synchronization with the sampling period ΔT, and stores it in the storage unit 23 together with the value of the counter i indicating the image acquisition order.
In step S13, it is determined whether or not there is a movement end signal 101 from the piezo element controller 9. If the movement end signal 101 is not received, the process returns to step S12.
If the movement end signal 101 has been received, the operation in step S1 in FIG. 3 is terminated, and the process proceeds to step S2 in FIG. That is, the candidate image acquisition unit 21 notifies the analysis candidate image group selection unit 24 that step S1 has been completed.
In this way, by repeating step S12, while the Fizeau lens 4 is being moved by the piezo element 8, m time-series images F ₁ , together with the value of the counter i that is position information on the time series, F ₂ ,..., F _m are sequentially stored in the storage unit 23.

Steps S2 to S4 constitute an analysis candidate image group selection step.
This step is regarded as having the phase increment Δφ as an analysis candidate image group G _k for calculating the shape of the measurement target surface 5 from the m time-series images F _i acquired in the candidate image acquisition step. This is a step of selecting a plurality of sets of five time-series images F _k , F _k1 , F _k2 , F _k3 , and F _k4 that can be used.

In step S2, as shown in FIG. 5, call each time series images F _i from the storage unit 23 by the analysis candidate image group selection section 24, in the luminance calculation position 32 which is a common position on each of the interference fringe image 31 Each luminance _Pi is acquired. That is, the luminance P _i represents a temporal luminance change at a certain position in the time series image F _i .
6, the position information i on the time series were plotted an example of the relationship between brightness P _i. The time-series image F _i is acquired at a constant sampling period ΔT, and a voltage proportional to time is applied to the piezo element 8. However, since the expansion and contraction characteristics of the piezo element 8 are nonlinear with respect to the applied voltage, Fizeau. The movement pitch of the lenses 4 is not equal. Therefore, the graph of the luminance P _i will be deviated from the sine wave.

Next, in step S3, the analysis candidate image group selection section 24, obtains the approximate curve 33 (see FIG. 6) of the graph of the luminance _{P i.} In the present embodiment, if the movement amount of the piezo element 8 is linear with respect to time, the approximate curve 33 is expressed by the following equations (5) and (6) using the fact that the luminance graph is a sine wave with respect to time. ).
_{f (i) = D 1 ·} i + D 2 · i 2 + D 3 · i 3 ··· (5)
p (i) = A.sin {f (i)} + B.cos {f (i)} + C (6)
Here, p (i) represents luminance, and f (i) represents the nonlinearity of the piezo element 8 by a cubic equation. D ₁ , D ₂ , D ₃ , A, B, and C are coefficients of the approximate expression. The variable i uses the value of the position information i on the time series corresponding to time as it is. f (i) is the time dimensionless rise time T, hours represents the phase variation amount with respect to image sequences F _1.
The coefficients D ₁ , D ₂ , D ₃ , A, B, and C can be obtained by performing known arithmetic processing such as Newton's method so as to minimize S in the following equation (7).

Since the approximate curve can be plotted on the graph as shown in FIG. 6 using the equations (5) and (6), the brightness P _i can be visually confirmed in this embodiment so that the approximation accuracy can be visually confirmed. Is displayed on the display unit 11 together with the actual measurement value.

Next, in step S4, the value of f (i) is closest to π / 2, π, 3π / 2, 2π using the expression (5) obtained in step S3 by the analysis candidate image group selection unit 24. Calculate the value of i. For example, when Equation (5) is represented by the phase change curve 41 shown in FIG. 7A, first, i = 10, 16 with i being phase shifted by π / 2 with respect to F _1. , 21, 26 are obtained. From these i values, an analysis candidate image group G ₁ = {F ₁ , F ₁₀ , F ₁₆ , F ₂₁ , F ₂₆ } used for wavefront calculation is selected.
Similarly, G ₂ , G ₃ ,... Are selected based on F ₂ , F ₃ ,.
In the present embodiment, as shown in FIG. 7B, a total of 20 G _k (k = 1,..., 20) up to G ₂₀ = {F ₂₀ , F ₂₅ , F ₂₉ , F ₃₄ , F ₃₈ }. ) Is elected.
Elected information of each G _k are is sent to the wavefront calculation unit 25.
The analysis candidate image group selection process is thus completed.

In the example of this embodiment, [pi / 2, that is, the moving distance of lambda / 8 are divided 9-4, the measurement position accuracy of the individual time-series images F _i is, lambda / 8 1 / 18-1 / 8, that is, about 4.4 nm to 9.9 nm, and higher accuracy than the positioning accuracy when the piezo element 8 is driven stepwise with each position as a target position is realized. Therefore, the measurement position accuracy is higher than in the past.
If the expansion / contraction characteristics of the piezo element 8 are linear characteristics, the position accuracy is about 5.3 nm, and the measurement position accuracy depends on the degree of nonlinear characteristics of the piezo element 8.
In order to improve the measurement position accuracy, the sampling period ΔT may be reduced by using a CCD with a higher video rate or increasing the rise time T of driving the piezo element 8.

Next, in step S5, a wavefront calculation step is performed.
This step is a step of analyzing a plurality of sets of analysis candidate image groups G _k selected in the analysis candidate image group selection step and calculating a wavefront according to each set of analysis candidate image groups G _k .
The wavefront calculation unit _25, G _k = with _{{F k, F k1, F} k2, F k3, F k4}, and calculates the wavefront corresponding to a surface shape by 5 bucket method. That is, for each position (x, y), the wavefront _kh is calculated using the above formulas (2) and (3) and stored in the storage unit 23. Then, the wavefront selection unit 26 is notified of the end of the wavefront calculation step, and the process proceeds to step S6.

Examples of wavefront calculation results are shown in FIGS. 8 (a), (b), (c), (d), and (e). These are analysis candidate images G ₁ (F _{1 to} F ₂₆ ), G ₅ (F _{5 to} F ₂₉ ), G ₁₀ (F _{10 to} F ₃₂ ), G ₁₅ (F _{15 to} F ₃₅ ), and G ₂₀ ( F _{20 to} F ₃₈ ). The (PV value and RMS value) of these wavefronts are (0.055λ, 0.012λ), (0.037λ, 0.006λ), (0.036λ, 0.003λ), and (0.050λ, 0), respectively. .006λ) and (0.069λ, 0.012λ).
Thus, the PV value and the RMS value of the wavefront h _k decrease with increasing k when 1 ≦ k ≦ 10, take the minimum value when k = 10, and increase with increasing k when 10 ≦ k ≦ 20. Showed changes.
This is because the relative positions of the wavefronts h _{k in} the optical axis direction of the Fizeau surface 4a and the measured surface 5 are different. As shown in FIG. 9, to represent the position on the optical axis of the collimated light 30a is focused by Fizeau lens 4 at point Q _R, the center of curvature Q _L of the surface to be measured 5, depending on the value of i, It is shifted by ΔZ in the direction of the optical axis C of the interferometer 51. Here, the optical path difference corresponding to the difference between the surface shape of the measurement surface 5 and Fizeau surface 4a to be measured surface reflected light 30c is generated, the reference position of the point Q _R and the center of curvature Q _L matches Only.
In the case of ΔZ> 0 (ΔZ <0), it is the same as that a reflecting surface having a larger (smaller) power than the surface to be measured 5 is disposed, and the wavefront h _k is such an apparent power level. Reflecting this, the wavefront aberration is greatly measured.

Next, in step S6, a wavefront selection process is performed.
In this step, the positional deviation amount ΔZ in the optical axis direction from the measurement reference position of the acquisition position of each analysis candidate image group G _k is evaluated from the information on each wavefront h _k calculated in the wavefront calculating step, and the positional deviation amount In this step, the wavefront having the smallest evaluation value of ΔZ is selected as the wavefront h representing the shape of the surface to be measured 5.
Wavefront selector 26, which is calculated by the wavefront calculation unit 25 calls the wavefront h _k from the storage unit 23, the wavefront h _k performs an operation of a polynomial approximation represented by the formula (1). By using the coefficient C ₃ calculated by this, from the equation (4), calculates the position displacement amount ΔZ corresponding to the wavefront h _k. Representing the positional deviation amount [Delta] Z _k.
After calculating ΔZ _k for all wavefronts h _k , _k that minimizes | ΔZ _k | is determined as _kmin . In the measurement example of the present embodiment shown in FIG. 8, _kmin = 10.
The wavefront selection unit 26 determines whether or not | ΔZ _kmin | is within a preset allowable value range of | ΔZ |, and if it is within the range, _selects the wavefront h _kmin as the wavefront h of the measured surface 5. The wavefront h _kmin is sent to the display control unit 27 and displayed on the display unit 11.
If | ΔZ _kmin | is not within the preset allowable range of | ΔZ |, there is a risk of a measurement error, so an error message is sent to the display control unit 27 and displayed on the display unit 11. Display.
Thus, the wavefront measurement by the wavefront measurement method of this embodiment is completed.

Thus, according to the wavefront measuring apparatus 50 of the present embodiment, a plurality of sets of analysis candidate image groups _Gk are selected from the m time-series images F _i , and each wavefront h _k is calculated. Since the wavefront that minimizes the evaluation value of the amount of positional deviation in the optical axis direction from the measurement reference position is _{obtained based on} the information on the wavefront h _k , even if a relative movement mechanism such as a piezo element 8 with poor repeated positioning accuracy is used, Accurate surface shape measurement can be performed.
Further, it is possible to perform easy and highly accurate measurement with a simple configuration without calibrating the piezo element 8 or performing feedback control by measuring the movement amount of the piezo element 8.
In addition, since calibration of the piezo element 8 is not required, there is an advantage that calibration costs and a period during which measurement cannot be performed due to calibration do not occur.
Further, since candidate images are acquired in synchronization with the video rate of the CCD 7, even if the number of candidate images is increased, measurement can be performed in a short time.
In addition, since the piezoelectric element 8 can be employed even if it has a low degree of nonlinearity or has a large variation in nonlinearity, an inexpensive element can be employed.
Further, in this embodiment, since the piezo element 8 is continuously driven in a certain direction, there is no variation in the movement position due to hysteresis characteristics, no position vibration at the time of stopping such as intermittent driving, etc. The corresponding movement position increases monotonically along the time series. Therefore, the measurement resolution can be reliably improved by increasing the number m of candidate images.

[Second Embodiment]
A wavefront measuring apparatus according to the second embodiment of the present invention will be described.
FIG. 10 is a schematic configuration diagram showing a schematic configuration of a wavefront measuring apparatus according to the second embodiment of the present invention. FIG. 11 is a functional block diagram showing a functional configuration of control means of the wavefront measuring apparatus according to the second embodiment of the present invention.

As shown in FIGS. 10 and 11, the wavefront measuring apparatus 50 </ b> A of the present embodiment is replaced with the measurement control unit 10 </ b> A and the piezoelectric element controller 9 instead of the measurement control unit 10 and the piezoelectric element controller 9 of the wavefront measuring apparatus 50 of the first embodiment. An element controller 9A is provided, and a strain gauge 8a (relative position information acquisition unit) is added.
The measurement control unit 10A is replaced with the candidate image acquisition unit 21, the movement control unit 22, and the analysis candidate image group selection unit 24 of the measurement control unit 10 of the first embodiment, and the candidate image acquisition unit 21A and the movement control unit 22A. An analysis candidate image group selection unit 24A is provided.
The piezo element controller 9A includes a calculation unit 35A instead of the calculation unit 35 of the piezo element controller 9 of the first embodiment, and a movement amount measurement unit 39 is added.
Hereinafter, a description will be given centering on differences from the first embodiment.

The strain gauge 8a is fixed to the piezo element 8 so that the strain in the expansion / contraction direction of the piezo element 8 can be measured.
The strain gauge 8a is connected to a movement amount measuring unit 39 provided in the piezo element controller 9A in order to measure the amount of expansion / contraction of the piezo element 8 from the output of the strain gauge 8a.
The movement amount measuring unit 39 detects the resistance change of the strain gauge 8a, calculates the strain change, calculates the expansion / contraction amount of the piezo element 8, and sends it to the calculation unit 35A.
The calculation unit 35A is electrically connected to the movement control unit 22A and the movement amount measurement unit 39, and in addition to the same function as the calculation unit 35 of the first embodiment, the piezo measured by the movement amount measurement unit 39 is used. Information on the amount of expansion / contraction of the element 8 can be converted into information on the movement position of the Fizeau surface 4a (hereinafter referred to as relative position information) and sent to the movement control unit 22A.
The measurement result of the movement amount measurement unit 39 may be used for position control of the piezo element 8 by the calculation unit 35A, but in the present embodiment, it is assumed that it is not used for position control of the piezo element 8.

Candidate image acquisition unit 21 </ b> A controls the timing of image capture of image acquisition unit 20 based on the operation input of operation unit 13, and based on information on the movement start position and movement end position set in advance from operation unit 13. The conditions for the movement operation of the movement control unit 22A are set, and a movement start signal is transmitted based on the operation input of the operation unit 13.
Then, when the image acquisition by the image acquisition unit 20 is started, the candidate image acquisition unit 21A converts each image data sent from the image acquisition unit 20 (hereinafter referred to as a candidate image) into information on their acquisition order, The information is stored in the storage unit 23 in association with the relative position information acquired from the movement control unit 22A. For example, when the i-th relative position information acquired in time series is q _i and the candidate image is H _i (where i = 1,..., M), the candidate image acquisition unit 21A sets the value of i. Accordingly, the relative position information q _i and the candidate image H _i can be respectively called up.

As in the first embodiment, the candidate image acquisition unit 21A may set the movement control unit 22A to change the command voltage in a certain direction at a constant speed. It may be changed. For example, after the measurement start position is assumed to be near the measurement reference position and driven in one direction to obtain a candidate image, the measurement start position may be returned to the vicinity of the measurement start position and driven in the opposite direction. . Alternatively, when the nonlinear characteristic of the piezo element 8 is approximately known, the command voltage change speed may be changed so that the nonlinearity is reduced.
As described above, in the present embodiment, the subscript i only represents the time-series order of candidate image acquisition, and does not represent the order of the positional relationship from which the candidate image _Hi was acquired. However, if the candidate images H _i are rearranged on the basis of the magnitude of the relative position information q _i , the time series image F _i is the same as that of the first embodiment.
In the following, for the sake of brevity, the relative position information and the candidate images rearranged in this way are newly added to q _j , H _j using subscripts j (where j = 1,..., M). I will represent it. Specifically, it is conceivable to store the conversion table from the subscript i to the subscript j in the storage unit 23 in order to actually rearrange the data once or to preserve the capture order.

The analysis candidate image group selection unit 24A, based on the relationship between the relative position information q _j and the candidate image H _j , the analysis candidate image group including n candidate images H _j that can be regarded as having a phase increment Δφ. G _k = {H _k , H _k1 ,..., H _{k (n−1)} } (where each subscript has a size of 1 to m, and the order of the sizes is k <k1 <. (N-1)) is selected. In the present embodiment, as in the first embodiment, an example of Δφ = π / 2 and n = 5 will be described as an example.
However, since the determination of the phase increment in this case is performed based on the relative position information q _j measured for each candidate image H _j , it is not necessary to calculate an approximate curve.

Next, the operation of the wavefront measuring apparatus 50A will be described focusing on the wavefront measuring method of the present embodiment.
FIG. 12 is a flowchart showing a measurement flow of the wavefront measuring method according to the second embodiment of the present invention.

According to the wavefront measuring apparatus 50A of the present embodiment, in the wavefront measuring method of the first embodiment, the relative position information q _j and the candidate image H are used instead of the time-series position information i and the time-series image F _i. By using _j , it is possible to measure the wavefront of the surface 5 to be measured by sequentially performing a candidate image acquisition step, an analysis candidate image group selection step, a wavefront calculation step, and a wavefront selection step. Hereinafter, the difference from the first embodiment will be mainly described along the measurement flow shown in FIG.

In step S31 (candidate image acquisition step), the relative position information q _j and the candidate image H _j are acquired and stored in the storage unit 23 in substantially the same manner as in the first step S1. However, the acquisition order of the candidate images _Hj may not match the time series order.

Step S34 constitutes an analysis candidate image group selection step.
This step is regarded as having the phase increment Δφ as the analysis candidate image group G _k for calculating the shape of the measurement target surface 5 from the m candidate images H _j acquired in the candidate image acquisition step. This is a step of selecting a plurality of sets of five candidate images H _k , H _k1 , H _k2 , H _k3 , and H _k4 that can be used.

In step S34, the analysis candidate image group selection section 24A, is converted to the phase amount by the relative position information q _j multiplied by a coefficient D = 4π / λ. The analysis candidate image group selection unit 24A then sets D · q _M (where M is an integer of k + 1 ≦ M ≦ m) to π / 2, π, where D · q _k is phase 0. The values of D · q _k1 ,..., D · q _k4 that are closest to 3π / 2 and 2π are calculated, and the analysis candidate image group G _k = {H _k , H _k1 , H _k2 , H _k3 used for wavefront calculation. , H _k4 }.
Here, for visual confirmation, a phase change curve in which _j is plotted on the horizontal axis and D · q _j is plotted on the vertical axis may be displayed on the display unit 11.
k is sequentially increased from 1, and is repeated until all analysis candidate image groups _Gk that can be selected are selected. Elected information of each G _k are is sent to the wavefront calculation unit 25.
The analysis candidate image group selection process is thus completed.

Next, step S35, S36 is a step for changing the time-series images _{F i} in the candidate image _{H j} in steps S5, S6 of the first embodiment.
Thus, the wavefront measurement by the wavefront measurement method of this embodiment is completed.

Thus, according to the wavefront measuring apparatus 50A of the present embodiment, a plurality of sets of analysis candidate image groups _Gk are selected from the m candidate images _Hj , and each wavefront _hk is calculated. Since the wavefront that minimizes the evaluation value of the positional deviation amount in the optical axis direction from the measurement reference position is obtained from the information of h _k , even if a relative movement mechanism such as a piezo element 8 with poor repeated positioning accuracy is used, high accuracy is obtained. Surface shape measurement can be performed.
Also includes a strain gauge 8a is relative position information acquisition unit, the information of the phase difference between the candidate image H _j, it is possible to determine from measurements by the strain gauges 8a, the phase difference is sufficiently small plurality of candidate images If it can drive so that can be acquired, a drive pitch, a drive order, etc. can be changed. For this reason, an easy and highly accurate measurement can be performed with a simple configuration without calibrating the piezo element 8 or performing feedback control by measuring the movement amount of the piezo element 8.
In addition, since the piezoelectric element 8 can be employed even if it has a low degree of nonlinearity or has a large variation in nonlinearity, an inexpensive element can be employed.
Further, in the analysis candidate image group selection step, the analysis candidate image group can be selected without performing the calculation for estimating the phase change curve, so that the calculation process is simplified.

[Third Embodiment]
A wavefront measuring apparatus according to a third embodiment of the present invention will be described.
FIG. 13 is a schematic configuration diagram showing a schematic configuration of a wavefront measuring apparatus according to the third embodiment of the present invention.

As shown in FIG. 13, the wavefront measuring apparatus 50B of the present embodiment includes an interferometer 52 made of a Twiman Green type optical system in place of the interferometer 51 of the wavefront measuring apparatus 50 of the first embodiment. The transmitted wavefront of the lens system 61 to be inspected is measured. Accordingly, the lens system 61 to be inspected is used, and a reference spherical surface 62 having a NA larger than that of the lens system 61 to be inspected is used as a reference surface. In this case, the surfaces to be measured of the lens system 61 to be inspected are all lens surfaces of the lens system 61 to be inspected. Therefore, this embodiment is an example in the case where there are a plurality of surfaces to be measured.
Hereinafter, a description will be given centering on differences from the first embodiment.

The interferometer 52 arranges a reference plane 60 composed of a high-precision plane reflecting surface on the optical path that transmits the beam splitter 3 out of the parallel light 30a that has been converted into parallel light by the collimator lens 2 in the interferometer 51, The reflected light 30 f (reference light) reflected by the reference plane 60 is reflected by the beam splitter 3 and travels toward the condenser lens 6.
On the other hand, on the optical path of the light reflected by the beam splitter 3 out of the parallel light 30a from the collimator lens 2 toward the beam splitter 3, a lens system 61 to be inspected, a reference spherical surface 62 (curved surface) from the side close to the beam splitter 3 Are arranged in this order.
The reference spherical surface 62 is supported by the piezo element 8 provided on the adjustment stage 12 so as to be movable in the optical axis direction.

According to such a wavefront measuring apparatus 50B, the divergent light emitted from the laser light source 1 is converted into the parallel light 30a by the collimator lens 2, and the transmitted light component transmitted toward the reference plane 60 by the beam splitter 3 Then, it is divided into reflected light components reflected toward the lens system 61 to be inspected.
The transmitted light component of the parallel light 30 a is reflected by the reference plane 60, travels backward in the optical path, and reaches the beam splitter 3. On the other hand, the reflected light component of the parallel light 30 a is imaged at the focal point of the lens system 61 to be inspected, diverges, reaches the reference spherical surface 62, is reflected, and reenters the lens system 61 to be inspected.
Here, at a position where the focal position of the lens system 61 to be inspected, which is the measurement standard position, coincides with the center of curvature of the reference spherical surface 62, the reflected light from the reference spherical surface 62 travels backward through the optical path and passes through the lens system 61 to be inspected. Then, the light is emitted as parallel light 30e (measurement light) toward the beam splitter 3.
Then, the reflected light 30 f reflected by the beam splitter 3 and the parallel light 30 e transmitted through the beam splitter 3 are combined on the optical axis of the interferometer 52 to form interference fringes, and are collected by the condenser lens 6. Then, interference fringes are projected on the imaging surface 7a of the CCD 7.
The interference fringes are formed by the parallel light 30e having wavefront aberration and the reflected light 30f, which is reference light having no wavefront aberration, by being transmitted twice through the lens system 61 to be inspected. Interference fringes representing wavefront aberration corresponding to errors in the surface shape of each surface to be measured in 61.

In the wavefront measuring method according to the present embodiment, the adjustment stage 12 aligns the reference spherical surface 62 and the lens system 61 to be inspected in the optical axis direction and the direction orthogonal to the optical axis, as in the first embodiment. After that, the piezo element 8 is expanded and contracted by the measurement control unit 10 and the piezo element controller 9, and the reference spherical surface 62 is moved in the optical axis direction from the measurement start position, and as shown in FIG. A candidate image acquisition process, an analysis candidate image group selection process, a wavefront calculation process, and a wavefront selection process are sequentially performed along the measurement flow.
The wavefront measuring method of the present embodiment performs relative movement between the measured surface and the reference surface by fixing the measured surface 5 and moving the Fizeau surface 4a by the piezo element 8 in the first embodiment. In this embodiment, the lens system 61 to be inspected is fixed, and the reference spherical surface 62 is moved by the piezo element 8 so that the relative movement between the measured surface and the reference surface is performed. The only difference is that Therefore, the details of each process are easily understood from the first embodiment, and the description thereof is omitted.

  As described above, according to the wavefront measuring apparatus 50B of the present embodiment, the transmitted wavefront of the lens system 61 to be inspected can be measured using the Twiman Green interferometer. As for the transmitted wavefront, highly accurate wavefront measurement can be performed using a relative movement mechanism such as the piezo element 8 with poor repeated positioning accuracy as in the first embodiment.

  In the above description, an example using a Fizeau interferometer or a Twiman Green interferometer has been described as an interferometer. It is not limited to an interferometer. For example, a Mach-Zehnder interferometer can be preferably used.

In the above description, in the wavefront selection step, ΔZ is obtained as an evaluation value of the amount of positional deviation in the optical axis direction using Equation (4). However, in this case, | ΔZ | is a coefficient C _3. Therefore, if the value of the positional deviation amount ΔZ is not required, the coefficient C ₃ itself is used as the evaluation value of | ΔZ | so that the calculation of the equation (4) is not performed by the wavefront selection unit 26. Good.

In the above description, the positional deviation amount, was evaluated by the equation (4) using the coefficients C ₃ is the power component when approximating the wave front by the formula (1), evaluation of the positional deviation amount to Is not limited.
For example, using the technique disclosed in Japanese Patent No. 2951366 (see the equations (1) and (2) of the same document), the wavefront is approximated by the following equation (9) and is a coefficient representing the defocus amount ( 2C ₃ -6C ₈ ) may be adopted as the evaluation value of the positional deviation amount.

  However, (ρ, θ) is polar coordinates when X = ρ cos θ and Y = ρ sin θ.

  In the above description, the wavefront calculation step has been described using an example of calculation using a so-called five-bucket method with n = 5. However, a seven-bucket method, a nine-bucket method with n = 7, 9, and 13, A 13-bucket method may be employed. If n is 3 or more, all known calculation methods used in the fringe scanning method can be similarly employed.

In the above description, the analysis candidate image group selection process has been described as selecting all analysis candidate image groups and then performing the wavefront calculation process to calculate the wavefront of each analysis candidate image group. This process may be repeated for some candidate images. For example, in the example of the first embodiment, first, as k = 1, elected analyzes candidate image group _{G 1,} and calculates the wavefront _{h 1} of _{G 1,} this, k = 2, ..., repeated up to 20 Thus, the analysis candidate image group selection step and the wavefront calculation step may be repeated for each k, and finally the wavefront selection step may be performed.
Further, after calculating the wavefront h _k (where k ≧ 2), ΔZ _k−1 and ΔZ _k are compared, and any one of the calculated values up to ΔZ _k according to a predetermined minimum value determination criterion, for example, , ΔZ _K (where 1 <K <k) is determined to be a minimum value, the wavefront h _K may be set as the wavefront h. In this case, the analysis candidate image group selection process, the wavefront calculation process, and the wavefront selection process are repeated for each k.

  In the above description, the example in which the strain gauge 8a is used as the relative position information acquisition unit has been described. However, if the relative position information acquisition unit can detect the movement amount in the optical axis direction of the measurement surface, It is not limited. For example, a capacitance sensor, a glass scale, a laser length measuring device, or the like may be employed.

  In the above description, the interferometer has been described as an example of the configuration of the Fizeau interferometer when the concave surface is used as the measurement surface, but the arrangement of the interferometer when the convex surface or the plane is the measurement surface, The configuration is well known, and the wavefront measuring method of the present invention can be used in any case.

  In the description of the first embodiment, the example in which the equations (5) and (6) are used as the approximate equations for calculating the phase change has been described. However, these are examples, and the optical element moving mechanism An approximate expression having an appropriate function shape can be employed depending on the movement characteristics. For example, the expression (5) may be an approximation expression of the second order or lower order or the fourth order or more with respect to i, and the expressions (5) and (6) may be expressed by one approximation expression.

  In the above description, the example in which the piezoelectric element 8 that is a piezoelectric element is used as the relative movement mechanism has been described. However, if the optical element can be moved by a minute amount at least in the range of about 1 to 2 wavelengths of the used wavelength. The piezoelectric element is not limited.

1 is a schematic configuration diagram showing a schematic configuration of a wavefront measuring apparatus according to a first embodiment of the present invention. It is a functional block diagram which shows the function structure of the control means of the wavefront measuring apparatus which concerns on the 1st Embodiment of this invention. It is a flowchart which shows the measurement flow of the wavefront measuring method which concerns on the 1st Embodiment of this invention. It is a flowchart explaining operation | movement of the candidate image acquisition process of the wavefront measuring method which concerns on the 1st Embodiment of this invention. It is a schematic diagram of the candidate image acquired at the candidate image acquisition process of the wavefront measuring method according to the first embodiment of the present invention. It is a typical graph which shows an example of the approximated curve in the candidate image acquisition process of the wavefront measuring method which concerns on the 1st Embodiment of this invention. It is a typical graph for demonstrating the selection method of an example of the analysis candidate image group of the analysis candidate image group selection process of the wavefront measuring method which concerns on the 1st Embodiment of this invention, and another example. The example of the wavefront calculated for every analysis candidate image group and displayed on the display part is shown. It is a schematic diagram for demonstrating position shift amount (DELTA) Z of an optical axis direction. It is a schematic block diagram which shows schematic structure of the wavefront measuring apparatus which concerns on the 2nd Embodiment of this invention. It is a functional block diagram which shows the function structure of the control means of the wavefront measuring apparatus which concerns on the 2nd Embodiment of this invention. It is a flowchart which shows the measurement flow of the wavefront measuring method which concerns on the 2nd Embodiment of this invention. It is a schematic block diagram which shows schematic structure of the wavefront measuring apparatus which concerns on the 3rd Embodiment of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Laser light source 2 Collimating lens 3 Beam splitter 4 Fizeau lens 4a Fizeau surface (reference surface which consists of curved surfaces)
5 Measurement surface 6 Condensing lens 7 CCD (imaging unit)
7a Imaging surface 8 Piezo element (relative movement mechanism)
9 Piezo element controller (piezo element drive unit)
DESCRIPTION OF SYMBOLS 10 Measurement control part 21 Candidate image acquisition part 22 Movement control part 23 Storage part 24 Analysis candidate image group selection part 25 Wavefront calculation part 26 Wavefront selection part 30a Parallel light (same light beam)
30b Transmitted light 30c Measurement surface reflected light (measurement light)
30d Reference surface reflected light (reference light)
30e Parallel light (measurement light)
30f Reflected light 50, 50A, 50B Wavefront measuring device 51, 52 Interferometer 61 Inspected lens system 62 Reference spherical surface (reference surface comprising a curved surface)
_Fi time-series images (candidate images)
_Gk analysis candidate image group H _i , H _j candidate image h, h _k wavefront ΔZ position shift amount

Claims (7)

The same light beam is divided into measurement light that is reflected or transmitted by a measurement surface made of a curved surface and reference light that interferes with the measurement light, and either the reference light or the measurement light is divided by a curved reference surface. The measurement light and the reference light are used to form interference fringes, and the measured surface and the reference surface are moved relative to each other in the optical axis direction to be regarded as having a constant phase increment. A wavefront measuring method of acquiring n (n is an integer of 3 or more) interference fringe images and measuring the wavefront of the measurement light using the n interference fringe images,
The relative position of the measurement surface and the reference surface in the optical axis direction is within a range including the measurement reference position in the optical axis direction in which the number of fringes of the interference fringes is minimized, and the phase difference between the measurement light and the reference light Is moved at a pitch finer than the certain phase increment, and the relative position information and m candidate images (m is an integer greater than n) that are candidates for the n interference fringe images, A candidate image acquisition step of acquiring
Of the m candidate images acquired in the candidate image acquisition step, n analysis candidate images for calculating the wavefront of the measurement light can be regarded as having n constant phase increments. An analysis candidate image group selection step of selecting a plurality of sets of candidate images;
Analyzing the plurality of sets of analysis candidate images selected in the analysis candidate image group selection step, respectively, and calculating a wavefront according to each set of analysis candidate images,
From the information of each wavefront calculated in the wavefront calculating step, the positional deviation amount in the optical axis direction from the measurement reference position of the acquisition position of each analysis candidate image group is evaluated, and the evaluation value of the positional deviation amount is the minimum And a wavefront selection step of selecting a wavefront as a wavefront of the measurement light. In the wavefront selection step,
Each wavefront calculated in the wavefront calculating step is approximated by a quadratic expression expressed by the following equation, and the positional deviation amount is evaluated from the magnitude of the coefficient of the quadratic term of the quadratic equation. The wavefront measuring method according to claim 1.
Z (X, Y) = C ₀ + C ₁ · X + C ₂ · Y + C ₃ · (X ² + Y ² ) (1)
Here, (X, Y, Z) is the coordinate value of the wavefront in the XYZ rectangular coordinate system in which the optical axis direction is the Z-axis direction, C ₀ is a constant term, C ₁ and C ₂ are primary terms, and C ₃ Is an approximation coefficient of a quadratic term. In the candidate image acquisition step,
While changing the relative position in the optical axis direction in one direction, acquiring the candidate images in time series at a constant sampling period, the information on the relative position is acquired as position information on the time series,
In the analysis candidate image group selection step,
An operation for estimating a relationship between position information on the time series and a phase from a plurality of candidate images that can be regarded as having the constant phase increment from a luminance change of interference fringes at a fixed position of the time series candidate images. The wavefront measuring method according to claim 1, wherein the wavefront measuring method is selected by performing. In the candidate image acquisition step,
By measuring the relative position in the optical axis direction while changing the relative position in the optical axis direction, the information on the relative position and the candidate image are obtained,
In the analysis candidate image group selection step,
3. The wavefront measuring method according to claim 1, wherein a plurality of candidate images that can be regarded as having the constant phase increment are selected based on information on the measured relative positions.   The wavefront measurement method according to claim 1, wherein the constant phase increment is π / 2 and the n is 5. The same light beam is divided into measurement light that is reflected or transmitted by a measurement surface made of a curved surface and reference light that interferes with the measurement light, and either the reference light or the measurement light is divided by a curved reference surface. Are obtained, and interference fringes are formed by the measurement light and the reference light, and n interference fringe images (n is an integer of 3 or more) that can be regarded as having a constant phase increment are obtained. A wavefront measuring apparatus having an interferometer and measuring a wavefront of measurement light using the n interference fringe images acquired by the interferometer,
The relative position of the measurement surface and the reference surface in the optical axis direction is within a range including the measurement reference position in the optical axis direction in which the number of fringes of the interference fringes is minimized, and the phase difference between the measurement light and the reference light A relative movement mechanism that moves so as to change at a pitch finer than the constant phase increment;
A relative position information acquisition unit that acquires information of the relative position from the relative movement mechanism;
A candidate image acquisition unit that acquires m (m is an integer greater than n) candidate images that are candidates for the n interference fringe images from the interferometer;
A storage unit for storing the relative position information acquired by the relative position information acquisition unit and the candidate image acquisition unit and the m candidate images in association with each other;
From among the information on the relative position and the m candidate images stored in the storage unit, the analysis candidate image group for calculating the wavefront of the measurement light may be regarded as having the constant phase increment. An analysis candidate image group selection unit for selecting a plurality of n candidate image sets,
Analyzing the plurality of sets of analysis candidate images selected by the analysis candidate image group selection unit, and calculating a wavefront according to each set of analysis candidate images,
From the information of each wavefront calculated by the wavefront calculator, the positional deviation amount in the optical axis direction from the measurement reference position of the acquisition position of each analysis candidate image group is evaluated, and the evaluation value of the positional deviation amount is the minimum And a wavefront selection unit that selects a wavefront as a wavefront of the measurement light. The wavefront selector is
Each wavefront calculated by the wavefront calculating unit is approximated by a quadratic expression expressed by the following equation, and the positional deviation amount is evaluated from the magnitude of the coefficient of the quadratic term of the quadratic equation. The wavefront measuring apparatus according to claim 6.
Z (X, Y) = C ₀ + C ₁ · X + C ₂ · Y + C ₃ · (X ² + Y ² ) (1)
Here, (X, Y, Z) is the coordinate value of the wavefront in the XYZ rectangular coordinate system in which the optical axis direction is the Z-axis direction, C ₀ is a constant term, C ₁ and C ₂ are primary terms, and C ₃ Is an approximation coefficient of a quadratic term.

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