Method and apparatus for measuring surface shape

Abstract

To provide a surface shape measuring method and a surface shape measuring device capable of shortening measuring time.SOLUTION: In a surface shape measuring method, an interferometer optical head for acquiring an interference fringe image generated by optical path difference between reference light and measuring light is used, N interference fringe images are acquired while scanning the interferometer optical head from a start point toward an end point in a Z-axis direction along an optical axis of the interferometer optical head relative to a measuring target surface, and a surface shape of a measurement target surface is measured based on the interference fringe images. In this measurement method, as for a common position in the N interference fringe images and with respect to an interference signal indicating change in interference light intensity along the Z-axis direction, a phase of interference fringe created by light of a predetermined analysis wavelength is obtained and a relative position in the Z-axis direction of the measurement target surface within a range of the analysis wavelength is specified based on the phase.SELECTED DRAWING: Figure 8

Description

Technical Field

[0001] The present invention relates to a method for measuring a surface shape and a surface shape measuring apparatus using an interferometer optical head.

Background Art

[0002] Conventionally, there has been known a surface shape measuring apparatus that precisely measures, for example, the surface shape of a measurement object using the luminance information of interference fringes generated by the interference of light.

[0003] For example, in a surface shape measuring apparatus using a light source that irradiates light with low coherence such as white light, at the in-focus position where the optical path lengths of the reference optical path and the measurement optical path match, the peaks of the interference fringes of each wavelength overlap and the luminance of the synthesized interference fringes increases. Therefore, in the surface shape measuring apparatus, while changing the optical path length of the reference optical path or the measurement optical path, an interference fringe image showing the two-dimensional distribution of the interference light intensity is photographed by an imaging device such as a CCD camera, and the in-focus position where the intensity of the interference light peaks at each measurement position within the photographed field of view is detected, whereby the height of the measurement surface (that is, the surface of the measurement object) at each measurement position is measured, and the surface shape of the measurement object can be measured (see, for example, Patent Document 1).

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] In the surface shape measuring device described above, the brightness of the interference light changes with a period approximately equal to the wavelength of the light causing the interference. Therefore, it is necessary to repeatedly capture interference fringe images while changing the optical path length of the reference optical path or the measurement optical path at intervals sufficiently finer than the wavelength. The surface shape measuring device then analyzes the accumulated interference fringe images, typically several hundred to a thousand, to determine the height of the measurement surface at each pixel position. This analysis includes a rough peak detection process that roughly detects the height at which the intensity of the interference light is maximum, and a fine peak detection process that determines the precise height.

[0006] In the rough peak detection process, for each pixel position constituting the interference fringe image, a signal waveform showing the change in brightness value with respect to the height position is obtained. Signal processing such as squaring, integration, and smoothing differentiation is applied to the signal waveform, and then a peak search is performed to find the height at which the intensity of the interference light is maximum. In the fine peak detection process, the detailed height of the measurement surface is determined by focusing on the phase of the signal waveform at each pixel position constituting the interference fringe image. Specifically, in the fine peak detection process, data around the interference area is extracted by the rough peak detection process, and then the phase is analyzed using FFT on the extracted data to analyze the peak of the interference signal.

[0007] Thus, conventional surface shape measuring devices required a significant amount of time for a single surface shape measurement because they had to capture numerous interference fringe images and then perform analysis on all of them. Furthermore, the analysis performed across a large number of accumulated images required a vast amount of work memory and high processing power. In addition, conventional fine peak detection processing could not be executed in parallel with rough peak detection processing.

[0008] Therefore, the present invention aims to solve the above problems and provide a surface shape measurement method and surface shape measuring apparatus that can suppress the work memory and computational processing power required for analysis processing, and consequently shorten the measurement time. [Means for solving the problem]

[0009] To solve the above problems, the surface shape measurement method according to the present invention uses an interferometer optical head that splits incoherent light irradiated from a light source into reference light to a reference mirror and measurement light to the surface to be measured using a beam splitter, and acquires interference fringe images generated by the optical path difference of the light reflected from each, and scans the interferometer optical head with respect to the surface to be measured in the Z-axis direction along the optical axis of the interferometer optical head from the starting point to the ending point, acquiring N (where N≧2) interference fringe images, and measures the surface shape of the surface to be measured based on the N interference fringe images. In this measurement method, for a common position in the N interference fringe images, the phase φ of the interference fringe created by light of a predetermined analysis wavelength Λ is determined for the interference signal consisting of N points that show the change in interference light intensity along the Z-axis direction, and the relative position Z of the surface to be measured in the Z-axis direction within the range of the analysis wavelength is determined based on the phase φ. FΛ Identify.

[0010] In this invention, the relative position Z in the Z-axis direction of the surface to be measured is FΛ Equation (1)

number

[0011] In this invention, the scan pitch in the Z-axis direction is z p The nth data point is counted from the starting point, and the Fourier transform F(Λ) of the interference signal f(z) at the analysis wavelength Λ is used. -1 ) is calculated based on equation (2),

number

[0012] In this invention, Λ = N·z, where ξ is an integer. p Select ξ and Λ such that / ξ, and then perform the discrete Fourier transform F(Λ -1 It is best to find ).

[0013] In the present invention, after obtaining the first interference fringe image, while sequentially obtaining the M-th (where 2 ≤ M ≤ N) interference fringe image, analysis processing for the interference fringe images up to the (M - 1)-th is performed, and after obtaining the N-th interference fringe image, analysis processing for the interference fringe images from the first to the N-th is performed. The analysis processing includes, at least for each position in the K-th interference fringe image obtained last, calculating Equation (3),

Equation

Equation

Equation

[0014] In the present invention, the absolute position Z in the Z-axis direction of the measurement target surface s is expressed as Z s = Λ×m + Z FΛ where m is an integer. The integer m is specified based on the Z-axis direction position Z of the measurement target surface obtained by a method different from the calculation of the relative position Z FΛ , and the absolute position Z R may be calculated by Z s = Λ×m + Z FΛ . s

[0015] In the present invention, m is (Z R - Z FΛIt is best to choose the integer closest to ) / Λ. In this case, the analytical wavelength Λ is k×2 n (However, k is an integer multiple of 2 or more than z is the scan pitch) p It is best to select a value that results in ( ).

[0016] In this invention, by integrating the square or absolute value of the interference signal, an integral curve consisting of N points is obtained to determine the starting noise line that approximates the starting noise area, which is the range where no interference occurs on the starting side of the measurement target surface; the ending noise line that approximates the ending noise area, which is the range where no interference occurs on the ending side of the measurement target surface; and the interference line that approximates the interference area, which is the range where interference occurs near the measurement target surface. Based on the starting noise line, the ending noise line, and the interference line, the Z-axis position of the measurement target surface is determined. R It would be good to find this.

[0017] In this invention, the analysis wavelength Λ is preferably selected from the vicinity of the wavelength at which the signal intensity is maximum when light irradiated from a light source is received by a photodetector for capturing interference fringe images. The analysis wavelength Λ is preferably between 290 nm and 350 nm. The analysis wavelength Λ is particularly preferably 320 nm.

[0018] Furthermore, the surface shape measuring device according to the present invention measures the surface shape of the surface to be measured of an object to be measured. The surface shape measuring device comprises an interferometer optical head that splits light emitted from a light source that emits incoherent light into reference light to a reference mirror and measurement light to the surface to be measured using a beam splitter, and acquires interference fringe images generated by the optical path difference of the light reflected from each using an image sensor, and an analysis means that determines the surface shape of the surface to be measured based on the interference fringe images acquired by the interferometer optical head. The interferometer optical head acquires N (where N≧2) interference fringe images on the surface to be measured by scanning it in the Z-axis direction along the optical axis of the interferometer optical head from a starting point to an ending point. The analysis means determines the phase of the interference fringe created by the light of the analysis wavelength Λ for the interference signal consisting of N points that show the change in interference light intensity along the Z-axis direction at a common position in the N interference fringe images acquired by the interferometer optical head, and determines the relative position Z in the Z-axis direction of the surface to be measured within the range of the analysis wavelength based on this phase. FΛ Identify. [Brief explanation of the drawing]

[0019] [Figure 1] This is a perspective view showing the overall configuration of the surface shape measuring device 1. [Figure 2] This is a schematic diagram showing the configuration of the interferometer optical head 152 along with its optical path. [Figure 3] This is an enlarged view of the main parts showing the structure of the objective lens section 22, the measurement optical path, and the reference optical path. [Figure 4] This is a block diagram showing the configuration of the computer unit 201. [Figure 5] Figure 5(a) shows an example of an interference signal, and Figure 5(b) shows an example of an integral curve w based on the interference signal. [Figure 6] This figure shows three straight lines (L1~L3) that approximate the integral curve, an intermediate line L4 calculated from these lines, and the position Zcross of the surface being measured. [Figure 7] This flowchart shows an example of the procedure for rough peak detection in surface shape measurement according to this embodiment. [Figure 8]This flowchart shows an example of the procedure for fine peak detection processing in surface shape measurement according to this embodiment. [Modes for carrying out the invention]

[0020] [Configuration of the surface shape measuring device] Hereinafter, a surface shape measuring device 1, which is a first embodiment of the surface shape measuring device 1 according to the present invention and combines an interference optical system and an image measuring device, will be described with reference to the drawings.

[0021] Figure 1 is a perspective view showing the overall configuration of a surface shape measuring device 1 according to the first embodiment. The surface shape measuring device 1 measures the surface shape of the object to be measured (workpiece) W. The surface shape measuring device 1 comprises a non-contact type image measuring machine 10 and a computer system 2 that drives and controls the image measuring machine 10 and performs necessary data processing. In addition to these, the surface shape measuring device 1 may also be appropriately equipped with a printer for printing out measurement results, etc.

[0022] The image measuring machine 10 comprises a stand 11, a sample stage 12, support arms 13a and 13b, an X-axis guide 14, and an imaging unit 15. As shown in Figure 1, the surface shape measuring device 1 is placed on a vibration isolation table 3 installed on the floor. The vibration isolation table 3 prevents vibrations from the floor from being transmitted to the surface shape measuring device 1 on the table. The vibration isolation table 3 may be either an active or passive type. The stand 11 is placed on the top plate of the vibration isolation table 3, and the stage 12 on which the workpiece W is placed is placed on it so that its upper surface is aligned with the horizontal plane as its base surface. In the following description, it will be assumed that the X and Y axes extend in directions parallel to the base surface of the stage 12, and the Z axis extends in a direction perpendicular to the base surface. The stage 12 is driven in the Y-axis direction by a Y-axis drive mechanism (not shown), and the workpiece W is movable in the Y-axis direction relative to the imaging unit. Support arms 13a and 13b, extending upward, are fixed to the center of both side edges of the mount 11, and an X-axis guide 14 is fixed so as to connect the upper ends of these support arms 13a and 13b. This X-axis guide 14 supports the imaging unit 15. The imaging unit 15 is driven along the X-axis guide 14 by an X-axis drive mechanism (not shown).

[0023] The imaging unit 15 includes an image optical head 151 for capturing a two-dimensional image of the workpiece W and an interferometer optical head 152 for measuring the surface shape of the workpiece W by optical interferometry. The workpiece W is measured at a measurement position set by the computer system 2 using either head. The measurement field of the image optical head 151 is usually set to be wider than that of the interferometer optical head 152, and the two heads can be switched between using control by the computer system 2. The image optical head 151 and the interferometer optical head 152 are supported by a common support plate to maintain a constant positional relationship, and are pre-calibrated to ensure that the measurement coordinate axes do not change before and after switching.

[0024] The image optical head 151, equipped with a CCD camera, illumination device, focusing mechanism, etc., captures a two-dimensional image of the workpiece W. The captured two-dimensional image data is input to the computer system 2.

[0025] Figure 2 is a schematic diagram showing the configuration of the interferometer optical head 152 along with its optical path. As will be described later, the interferometer optical head 152 acquires interference fringe images generated by the optical path difference of light reflected from the measurement optical path and the reference optical path using an image sensor. As shown in Figure 2, the interferometer optical head 152 is configured as a Michelson type interferometer and comprises a light emission unit 20, an illumination light guide unit 21, an objective lens unit 22, an imaging lens 24, an imaging unit 25, and a drive mechanism unit 26.

[0026] The light-emitting unit 20 is a light source that emits low-coherence (incoherent) light. Here, low-coherence light is, for example, light with a coherence length of about 100 μm or less. The light-emitting unit 20 has a wide bandwidth (for example, wavelengths of 500 to 800 nm) and outputs broadband light with low coherence that has many wavelength components. Examples of light-emitting units 20 include lamp light sources such as halogens, LEDs (Light Emitting Diodes), and SLDs (Super Luminescent Diodes). The light emitted by the light-emitting unit 20 is preferably white light, for example, but is not limited to this as long as it is low-coherence light.

[0027] The illumination light guide unit 21 includes a beam splitter 211 and a collimator lens 212. Light emitted from the light emission unit 20 is directed parallel to the beam splitter 211 via the collimator lens 212 from a direction perpendicular to the optical axis of the objective lens unit 22, and light is emitted from the beam splitter 211 along the optical axis, illuminating the objective lens unit 22 from above with a parallel beam.

[0028] The objective lens section 22 comprises an objective lens 221, a beam splitter 222, a reference mirror section 223, and the like. The reference mirror section 223 also includes a reference mirror 224 at a predetermined position. In the objective lens section 22, when a parallel beam is incident on the objective lens 221 from above, the incident light becomes focused light at the objective lens 221 and is incident on the reflective surface 222a inside the beam splitter 222.

[0029] The incident light is split by the beam splitter 222 into reflected light (reference light) traveling along the reference optical path in the reference mirror section 223 and transmitted light (measurement light) traveling along the measurement optical path where the workpiece W is placed. The reflected light is reflected by the reference mirror 224 and then reflected again by the reflective surface 222a of the beam splitter 222. Meanwhile, the transmitted light is focused and reflected by the workpiece W and passes through the reflective surface 222a of the beam splitter 222. The reflected light from the reference mirror 224 and the reflected light from the workpiece W are combined by the reflective surface 222a of the beam splitter 222 to form a composite wave.

[0030] The combined wave, formed at the reflective surface 222a of the beam splitter 222, becomes a parallel beam in the objective lens 221 and travels upward, passing through the illumination light guide 21 and entering the imaging lens 24 (dotted line in Figure 2). The imaging lens 24 focuses the combined wave and forms an interference fringe image on the imaging unit 25.

[0031] The imaging unit 25 is a CCD camera or the like consisting of a two-dimensional image sensor that constitutes the imaging means, and it captures an interference fringe image of the composite wave (reflected light from the workpiece W and reflected light from the reference mirror 224) output from the objective lens unit 22.

[0032] Figure 3 is an enlarged view of the main part of the objective lens section 22. The drive mechanism section 26 corresponds to the optical path length variable means of the present invention, and moves the interferometer optical head 152 in the optical axis direction according to a movement command from the computer system 2. Figure 3 shows a state in which the optical path lengths of the reference optical path (dashed line) and the measurement optical path (solid line) are equal. During measurement, interference fringe images are taken while moving the interferometer optical head 152 in the optical axis direction (i.e., the Z axis direction), thereby acquiring many interference fringe images with different measurement optical path lengths. Interference occurs when the difference between the length of the measurement optical path and the length of the reference optical path is less than or equal to the coherent length from the light source, and the interference intensity is strongest (i.e., the contrast of the interference fringes is maximized) when the length of the measurement optical path matches the length of the reference optical path. In the above explanation, the case in which the interferometer optical head 152 is moved was used as an example, but the length of the measurement optical path may also be adjusted by moving the stage 12. Alternatively, the length of the reference optical path may be made variable by moving the reference mirror 224 in the optical axis direction (i.e., the left and right direction in Figure 3). Thus, in the interferometer optical head 152, the optical path length of either the reference optical path or the measurement optical path is made variable.

[0033] The interferometer optical head 152 is moved and scanned in the optical axis direction by the drive mechanism 26 under the control of the computer system 2, and the imaging unit 25 takes an image each time it moves a predetermined distance. The interference fringe images are sequentially transferred to and acquired by the computer system 2.

[0034] Returning to Figure 1, the computer system 2 comprises a computer main unit 201, a keyboard 202, a joystick box (hereinafter referred to as J / S) 203, a mouse 204, and a display 205. The computer system 2 determines the surface shape of the surface to be measured based on the interference fringe image acquired by the interferometer optical head 152. The computer system 2 functions as an analysis means in the present invention.

[0035] Figure 4 shows a block diagram illustrating the configuration of the computer main unit 201. As shown in Figure 4, the computer main unit 201 comprises a CPU 40 that forms the core of the control system, a storage unit 41, a work memory 42, interfaces (indicated as "IF" in Figure 5) 43, 44, 45, and 46, and a display control unit 47 that controls the display on the display 205.

[0036] Operator instructions entered via keyboard 202, J / S 203, or mouse 204 are input to CPU 40 via interface 43. Interface 44 is connected to image measuring machine 10 and supplies various control signals from CPU 40 to image measuring machine 10, and receives various status information and images from image measuring machine 10 and inputs them to CPU 40.

[0037] When the image measurement mode is selected, the display control unit 47 displays an image on the display 205 obtained from the image signal supplied from the CCD camera of the image optical head 151. When the optical interference measurement mode is selected, the display control unit 47 displays images captured by the interferometer optical head 152, surface shape data measured by the interferometer optical head 152, etc., on the display 205 as appropriate based on control by the CPU 40. The measurement results from the image optical head 151 and the interferometer optical head 152 can be output to a printer via the interface 45.

[0038] The work memory 42 provides a workspace for various processes performed by the CPU 40. The storage unit 41 is composed of, for example, a hard disk drive or RAM, and stores programs executed by the CPU 40, measurement results from the surface shape measuring device 1, etc. The programs executed by the CPU 40 include programs that perform the analysis processing described later.

[0039] Based on various input information via each interface, operator instructions, and programs stored in the memory unit 41, the CPU 40 performs various processes such as switching between the image measurement mode using the image optical head 151 and the optical interference measurement mode using the interferometer optical head 152, specifying the measurement range, moving the imaging unit 15 in the X-axis direction, moving the stage 12 in the Y-axis direction, capturing a two-dimensional image with the image optical head 151, measuring interference fringe images with the interferometer optical head 152, and calculating the surface shape.

[0040] When calculating the surface shape, the CPU 40 identifies the moving scan position where the interference fringe peak occurs for each pixel position in the interference fringe image, and sets this as the height (position in the Z-axis direction) at each pixel position in the interference fringe image.

[0041] Next, a method for determining the height at each pixel position in the interference fringe image using the surface shape measuring device 1 of this embodiment will be described. In the following, the interferometer optical head 152 is scanned in the Z-axis direction along the optical axis from a starting point (for example, the position closest to the workpiece W in the scanning range in the Z-axis direction) to an ending point (for example, the position furthest from the workpiece W in the scanning range in the Z-axis direction) to acquire N interference fringe images (where N≧2). Then, the height (Z-axis direction position) at each pixel position is determined based on the N interference fringe images acquired in this way. From the determined heights at each pixel position, the surface shape of the workpiece W can be determined.

[0042] [Rough peak detection process] First, the rough peak detection process will be explained. In the rough peak detection process of this embodiment, for common pixel positions in N interference fringe images, a signal indicating the change in interference light intensity (pixel brightness value) at each imaging position along the Z-axis is defined as the interference signal (Figure 5(a)). The square of this interference signal or the absolute value of the interference signal is obtained, and the height (Z-axis position) at each pixel position is determined from the integral curve obtained by integrating this value.

[0043] In the method of this embodiment, such an integral curve is approximated by three straight lines, as shown in Figure 6: a starting noise line L1, an interference line L2, and an ending noise line L3. The starting noise line L1 approximates the starting noise section, which is the range where no interference occurs on the starting side of the measurement target surface. The ending noise line L3 approximates the ending noise section, which is the range where no interference occurs on the ending side of the measurement target surface. The interference line L2 approximates the interference section, which is the range where interference occurs in the vicinity of the measurement target surface.

[0044] The starting noise line L1 can be determined based on a predetermined number of points (e.g., 10 points) from the starting point of the integral curve. The ending noise line L3 can be determined based on a predetermined number of points (e.g., 10 points) from the ending point of the integral curve. Furthermore, the starting noise line L1 and the ending noise line L3 can be determined under the constraint that their slopes are equal.

[0045] The interference line L2 can be defined as the line with the maximum slope among the approximate lines for a predetermined number of consecutive points on the integral curve. For example, the approximate line can be found by applying the least squares method to all of the predetermined number of consecutive points. Alternatively, the approximate line can be defined as the line connecting the endpoints of the predetermined number of consecutive points.

[0046] Then, the position (height) in the Z-axis direction of the surface to be measured is determined based on the starting noise line L1, the ending noise line L3, and the interference line L2. Specifically, an intermediate line L4 is determined that has a slope obtained by averaging the slopes of the starting noise line L1 and the ending noise line L3, and an intercept obtained by averaging the intercepts of the starting noise line and the ending noise line. Then, the intersection Z of the intermediate line L4 and the interference line L2 is determined. cross Determine the position of this intersection and the position (height) in the Z-axis direction of the surface to be measured. R Let's assume that.

[0047] Applying the above method to all pixels in the interference fringe image, the position Z in the Z-axis direction is determined.R By determining this, the surface shape of the workpiece W can be obtained.

[0048] The position of the surface to be measured in the Z-axis direction Z R The height can be obtained from the integral curve using the method described above, but the analysis process to determine the height at the pixel position can be started before all N points constituting the integral curve are obtained (i.e., before all N interference fringe images have been captured). In the following, referring to the flowchart shown in Figure 7, a method will be described in which at least part of the analysis process is performed using interference fringe images already stored in the computer system 2, while capturing interference fringe images with the interferometer optical head 152 and transferring them to the computer system 2, before all N interference fringe images are obtained. This method can shorten processing time and reduce processing load.

[0049] As already explained, the surface shape measuring device 1 sequentially acquires N (where N≧2) interference fringe images while scanning in the Z-axis direction along the optical axis of the interferometer optical head 152 from the starting point to the ending point, and transfers them to the computer system 2. In the rough peak detection process using this method, when the surface shape measuring device 1 starts the measurement, it first acquires the first interference fringe image (step S10). Subsequently, it sequentially acquires the M (where 2≦M≦N) interference fringe images while scanning the position of the interferometer optical head 152, and in parallel with this, the computer system 2 performs analysis processing on the interference fringe images up to M-1 (step S20).

[0050] The analysis process for interference fringe images up to the M-1th image includes an integral curve update process (step S21) that determines the value of the M-1th point from the starting point of the integral curve for each position in the M-1th interference fringe image acquired last. This integral curve update process determines the M-1th point on the integral curve by adding the squared luminance value to the integral value up to the M-2nd image for each position in the M-1th interference fringe image. Note that the initial value of the integral value (i.e., the integral value up to the M-2=0th image, to which the squared luminance value is added when M=2) is set to 0.

[0051] Furthermore, the analysis process for interference fringe images up to M-1 includes a process to calculate the latest approximate line (step S22) for a predetermined number of consecutive points that include the M-1 point of the integral curve as the point closest to the endpoint. If M-1 is less than the predetermined number, the process to calculate the latest approximate line does not need to be performed.

[0052] Furthermore, the analysis process for interference fringe images up to the M-1th image includes a provisional interference line update process (step S23) that finds the provisional interference line with the maximum slope among the approximate lines for a predetermined number of consecutive points up to the M-1th point of the integral curve. This provisional interference line update process compares the provisional interference line obtained for the M-2nd point of the integral curve with the approximate line obtained in the latest approximate line calculation process, and the one with the larger slope is adopted as the new provisional interference line. Note that if M-1 is less than the predetermined number, the provisional interference line update process does not need to be performed.

[0053] In this way, by acquiring the Mth interference fringe image while simultaneously performing analysis on the M-1 interference fringe images already acquired, it is possible to proceed with part of the process of determining the height of the surface to be measured before acquiring all N interference fringe images.

[0054] If the Nth interference fringe image has not yet been acquired after step S20 (step S30; No), the process returns to step S20 to acquire the next interference fringe image while simultaneously performing analysis on the acquired interference fringe images.

[0055] Step S20 is repeated until the Nth interference fringe image is obtained (Step S30; Yes), and then analysis processing (Step S40) is performed on the first to Nth interference fringe images. The analysis processing for the first to Nth interference fringe images includes an integral curve update process to find the value of the Nth point in the integral curve (Step S41), a latest approximate line calculation process (Step S42), and a provisional interference line update process (Step S43). The provisional interference line obtained in the provisional interference line update process in the analysis processing for the first to Nth interference fringe images is defined as the interference line.

[0056] In this way, once the Nth interference fringe image is acquired, the integral curve up to the (N-1)th point, which has already been acquired, and a provisional interference line based on the integral curve up to the (N-1)th point can be determined. Then, after acquiring the Nth interference fringe image, the entire integral curve can be determined simply by finding the Nth point (the last point) in the integral curve. Furthermore, by finding an approximate line that includes the Nth point and comparing it with the provisional interference line based on the integral curve up to the (N-1)th point, the final interference line can be obtained.

[0057] Furthermore, in the analysis process after acquiring the Nth interference fringe image, the starting point noise line L1 and the ending point noise line L3 are determined based on a predetermined number of points from the starting point of the integral curve and a predetermined number of points from the ending point of the integral curve (step S44).

[0058] If the constraint that the slopes of the starting noise line L1 and the ending noise line L3 are equal is not imposed, the starting noise line L1 may be determined in the analysis process for the interference fringe images up to M-1 when M-1 matches the number of points required to determine the starting noise line L1, and the ending noise line L3 may be determined in the analysis process after obtaining the Nth interference fringe image.

[0059] In the analysis process after obtaining the Nth interference fringe image, the intermediate line is then calculated from the starting noise line L1 and the ending noise line L3 (step S45). Furthermore, the intersection point of the intermediate line and the interference line is found, and the position Z of this intersection point is determined. cross The position (height) of the surface to be measured in the Z-axis direction Z R (Step S46)

[0060] Thus, after determining the interference line, the height of the surface to be measured can be determined by a process that has a relatively low processing load and does not require a large amount of work memory, such as linear approximation with a relatively small number of points and calculation of intersection points between lines.

[0061] As described above, the surface shape measuring device 1 according to this embodiment can suppress the work memory and computational processing power required for analysis processing in the rough peak detection process. Furthermore, by performing interference fringe image acquisition and analysis processing in parallel, the measurement time can be shortened.

[0062] [Fine peak detection process] Next, the fine peak detection process will be explained. In the fine peak detection process of this embodiment, the relative position (height) in the Z-axis direction of the surface to be measured is accurately determined by focusing on the phase of the interference signal.

[0063] As already mentioned, the low-coherence (incoherent) light emitted from the light emission unit 20 is light in which various wavelengths of light are mixed in a certain proportion, as is typical of white light, and its coherence has been intentionally lowered. Because incoherent light contains multiple wavelengths in this way, interference fringes are generated only when the length of the measurement light path reflected by the workpiece W and the length of the reference light path reflected by the reference mirror are approximately equal.

[0064] However, since the incoherent light emitted from the light emission unit 20 has a wide wavelength band, if the wavelength band distribution contained in the reflected light changes due to factors such as the color and shape of the workpiece surface, it directly leads to distortion of the interference signal and becomes a factor in measurement errors. In addition, it is difficult to define the phase of incoherent light that contains multiple wavelength components. Due to these factors, the phase obtained by directly analyzing the interference signal created by incoherent light cannot be said to be highly accurate. Therefore, in the fine peak detection process of this embodiment, a component of a specific analysis wavelength Λ is extracted from the wavelength band of the light source and analyzed. Then, from the phase of the analysis wavelength obtained in this way, it is possible to accurately determine the relative position (height) in the Z-axis direction of the surface to be measured. Here, relative position means the position within a range of one wavelength of the analysis wavelength Λ.

[0065] To perform phase analysis on a specific analytical wavelength Λ among the wavelength components contained in the incoherent light emitted from the light emission unit 20, the interference signal is Fourier transformed, and the analytical wavelength Λ contained in the interference signal is analyzed. As a method for Fourier transforming the interference signal, the Fast Fourier Transform (FFT) is used in conventional fine peak detection processing. Although FFT requires less computation and enables high-speed calculation due to convolution, it requires 2 data points. n There is a constraint that the number of data points must be a certain number, and that the interval must be a periodic function. If the interval is not periodic, a method is known to use a window function to blur the beginning and end of the interval to make it appear as a pseudo-periodic function, but using a window function makes it impossible to avoid the occurrence of analytical errors. Therefore, in this embodiment, the Discrete Fourier Transform (DFT) is used to perform phase analysis on the analysis wavelength Λ. Since the DFT does not perform convolution, the constraint on the number of data points is relaxed. On the other hand, it is known that the DFT takes longer to compute than the FFT, but in this embodiment, since the DFT is applied only to the selected analysis wavelength Λ, the increase in computation time is limited.

[0066] In the interference optical system of the interferometer optical head 152, when the interferometer optical head 152 is displaced, the optical path lengths of both the incident optical path to the workpiece W and the reflected optical path change. Therefore, when the light reaches the imaging unit 25, an optical path difference equal to twice the displacement of the interferometer optical head 152 occurs. Thus, the wavelength of the interference light becomes half the wavelength of the light source, and if the wavelength of the light source is λ and the analytical wavelength included in the interference signal is Λ, then the relationship is Λ = λ / 2.

[0067] In the following, we consider the case where we perform an analysis on the analytical wavelength Λ included in the interference signal.

[0068] The shape error in surface shape measurement using the above method tends to decrease as the intensity of the interference signal detected by the imaging unit 25 increases. Therefore, the analysis wavelength Λ should be selected from the vicinity of the wavelength at which the intensity of the interference signal detected by the imaging unit 25 is maximum. For example, Λ is good if it is between 260 nm and 400 nm, even better if it is between 290 nm and 350 nm, and particularly good if it is 320 nm.

[0069] Equation (6) shows the definition for performing a Fourier transform on the data function f(z) of the interference signal.

number

[0070] Here, the interferometer optical head 152 scans at a pitch z p Assume that images are acquired at equal intervals. If n is the imaging number of the interferometric image, then z in equation (6) is n·z p It can be replaced with this, and equation (6) can be transformed into a discrete sum as shown in equation (7).

number

[0071] By introducing an integer ξ and the total number of images N, we can define Λ as N·z p By substituting / ξ, equation (7) can be transformed into equation (8).

number

[0072] For example, total number of images N=500, scan pitch z p Let's consider the case where we set Λ = 50 nm and analyze the region near Λ = 300 nm. In this case, Λ = N·z p We select ξ and Λ such that / ξ. Ideally, we want to analyze light at exactly Λ = 300 nm. However, DFT is limited to handling only discrete wavelengths of Λ = 50 × 500 / ξ, so to minimize error, we select Λ = 301.205 nm (ξ = 83). In equation (8), N = 500, z p Substituting ξ=50nm and ξ=83, we obtain the expression shown in equation (9).

number

[0073] F(Λ -1 ) becomes a complex number, and F(Λ -1 This can be expressed as ||F(Λ) = a + bi. In this case, the interference fringe intensity produced by light of the analytical wavelength Λ is I = |F(Λ) -1 )| 2 =|a+bi| 2 =a 2 +b 2 It is calculated as follows. Furthermore, its phase is F(Λ -1 The argument of ) is calculated as shown in equation (10).

[0074]

number

[0075] Then, the relative position (height) in the Z-axis direction is determined from the interference signal. FΛ This can be obtained by converting the phase obtained in equation (10) into the dimension of length using equation (1).

[0076]

number

[0077] The Z-axis position of the measurement target surface determined by the fine peak detection process. FΛ The fine peak detection process can be performed in parallel with the rough peak detection process described earlier. This process can be performed before all N points constituting the interference signal are acquired (i.e., before all N interference fringe images have been captured). The following describes a method in which, while acquiring interference fringe images with the interferometer optical head 152 and transferring them to the computer system 2, at least part of the analysis process is performed using interference fringe images already stored in the computer system 2, before all N interference fringe images are acquired. This method can shorten processing time and reduce processing load. Furthermore, this fine peak detection process can be performed in parallel with the rough peak detection process described earlier.

[0078] As already explained, the surface shape measuring device 1 sequentially acquires N (where N≧2) interference fringe images while scanning in the Z-axis direction along the optical axis of the interferometer optical head 152 from the starting point to the ending point, and transfers them to the computer system 2. In the fine peak detection process using this method, when the surface shape measuring device 1 starts the measurement, it first acquires the first interference fringe image (step S110). Subsequently, it sequentially acquires the M (where 2≦M≦N) interference fringe images while scanning the position of the interferometer optical head 152, and in parallel with this, the computer system 2 performs analysis processing on the interference fringe images up to M-1 (step S120).

[0079] The analysis process for interference fringe images up to M-1 includes at least a Fourier transform (step S121). This Fourier transform calculates the value of equation (3) for each position in the last acquired K-th interference fringe image.

number

number

[0080] This allows for the Fourier transform F(Λ) at the analytical wavelength Λ for the first K points. -1 We calculate equation (5), which is the discrete sum of ). Note that the initial value of the discrete sum is 0.

number

[0081] If the Nth interference fringe image has not yet been acquired after step S120 (step S130; No), the process returns to step S120 to acquire the next interference fringe image while simultaneously performing analysis on the acquired interference fringe images.

[0082] After repeating step S120 until the Nth interference fringe image is obtained (step S130; Yes), an analysis process (step S140) is performed on the first to Nth interference fringe images. The analysis process on the first to Nth interference fringe images includes the same Fourier transform process as described above (step S141). The discrete sum obtained in the Fourier transform process in the analysis process performed after obtaining the Nth interference fringe image is the Fourier transform F(Λ) of the interference signal f(z) at the analysis wavelength Λ. -1 )

[0083] Furthermore, the analysis process for the interference fringe images from the first to the Nth image is performed using the aforementioned equation (5) F(Λ -1 The phase of ) is calculated (step S142), and the coordinates (height) of the surface to be measured are calculated using the aforementioned equation (1) Z FΛ We find this (step S143).

[0084] By doing this, when the Nth interference fringe image is acquired, the Fourier transform F(Λ) at the analysis wavelength Λ up to the (N-1)th point already acquired can be obtained. -1 The discrete sum of ) can be calculated. Then, after obtaining the Nth interference fringe image, the Fourier transform F(Λ -1 By simply reflecting the Nth point (the last point) in the discrete sum of ), the Fourier transform F(Λ) of the interference signal f(z) at the analytical wavelength Λ is obtained.-1 This allows for the determination of the position of the target surface. In this way, fine peak detection can be performed using a process that has a relatively low processing load and does not require a large amount of work memory, thereby determining the relative position of the surface being measured.

[0085] As described above, the surface shape measuring device 1 according to this embodiment can suppress the work memory and computational processing power required for analysis processing in the fine peak detection process. Furthermore, by performing interference fringe image acquisition and analysis processing in parallel, the measurement time can be shortened.

[0086] The analysis process for the fine peak detection process shown in the flowchart in Figure 8 can be performed in parallel with the analysis process for the rough peak detection process shown in the flowchart in Figure 7. That is, step S20 in Figure 7 and step S120 in Figure 8 can be performed in parallel, and step S40 in Figure 7 and step S140 in Figure 8 can be performed in parallel. Therefore, after acquiring the Nth interference fringe image, the coordinate (height) Z of the measurement target surface can be determined by rough peak detection with minimal processing. R and the relative position (height) of the measurement target surface in the Z-axis direction by fine peak detection. FΛ It is possible to find this.

[0087] [Combination of rough peak detection and fine peak detection] In the fine peak detection process described above, the position in the Z-axis direction is determined based on the phase φ of the interference signal for a specific analysis wavelength Λ. Therefore, the determined position is the relative position Z in the Z-axis direction of the measurement target surface within the range of the analysis wavelength. FΛ Therefore, the range of heights that can be identified by the fine peak detection process alone is limited to the range from -Λ / 2 to +Λ / 2. In other words, the absolute position (true position) Z of the surface being measured. S Let m be an integer, Z S =Λ×m+Z FΛ When expressed as such, if an integer m can be specified, the relative position Z obtained by the fine peak detection process can be determined. FΛ From absolute position Z S It is possible to find this.

[0088] Therefore, the height Z identified by the rough peak detection process R Therefore, we can find the optimal value of m using equation (11).

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[0089] In other words, m is (Z R -Z FΛ It is the integer closest to ) / Λ.

[0090] Using the m obtained in this way, the absolute position Z of the surface to be measured is S is, Z S =Λ×m+Z FΛ This can be determined by [method].

[0091] Thus, when determining the absolute position of the surface to be measured using equation (11), division is necessary. Many arithmetic units (especially those that cannot perform floating-point processing) will perform fixed-point division, but fixed-point division is time-consuming because it involves many processing steps. To solve this problem, we set k to the scan pitch z p The divisors of (i.e., k is an integer multiple of 2 or more) of the scan pitch z p When the analytical wavelength Λ is set to k×2 (where the value is k×2), n It is preferable to select such a combination.

[0092] In equation (11), Z R = Z R_index ·z p Z FΛ = Z FΛ_phase Let Λ be the same as Z. R_index is, Z R The scan pitch is z p An integer representing how many times Z FΛ_phase This is the phase of light at the analytical wavelength Λ (the same as Φ / 2π obtained from Φ in equations (1) and (10)). At this time, the scan pitch z p Using k, which is a divisor of z, p=k·z p ’ can be expressed as. And when the analysis wavelength Λ is selected such that Λ = 2 n ·k, Equation (11) can be transformed as in Equation (12).

[0093]

Number

[0094] Thus, when the analysis wavelength Λ is selected such that Λ = 2 n ·k, the division for obtaining m will use 2 n as the divisor. Generally, in an arithmetic unit, division using 2 n as the divisor can be replaced by an n-bit bit shift operation. Therefore, by setting the analysis wavelength Λ in this way, division that requires many processing steps and takes a long time can be eliminated, and the processing time can be shortened.

[0095] 〔Modification of Embodiment〕 Note that the present invention is not limited to the above-described embodiment, and modifications, improvements, etc. within the scope that can achieve the object of the present invention are included in the present invention. For example, in the above embodiment, an image measurement apparatus using a Michelson interferometer was described as an example. However, the present invention can also be applied to various measurement apparatuses and microscopes using interferometers other than image measurement apparatuses. Further, the present invention can also be applied to measurement apparatuses using other equal optical path interferometers such as the mirror type, Fizeau type, and Twyman-Green type.

[0096] Also, in the above embodiment, the analysis processing in the rough peak detection processing and the fine peak detection processing was performed by the computer system 2, but part or all of the analysis processing may be realized by dedicated hardware using an ASIC or FPGA.

[0097] Also, in the above embodiment, the absolute position Z FΛ was obtained from the relative position Z R obtained in the fine peak detection processing and the position Z S obtained in the rough peak detection processing. However, the relative position Z FΛAnd the absolute position Z from the position determined by a different method than described above. S You may also find the relative position Z obtained by the fine peak detection process described above, compared to the position obtained by the conventional rough peak detection method. FΛ and absolute position Z S You may also request this.

[0098] Furthermore, any modifications made by those skilled in the art to the aforementioned embodiments, including additions, deletions, or design changes to components, or combinations of features from each embodiment, are also included within the scope of the present invention, as long as they retain the essence of the present invention. [Industrial applicability]

[0099] The present invention, when applied to an optical interferometry device, makes it possible to reduce the number of interference fringe images taken and shorten the measurement time. [Explanation of Symbols]

[0100] 1...Surface shape measuring device 2. Computer Systems 3. Vibration isolation table 10. Image measuring machine 11. Stand 12 stages 13a, 13b... Support arms 14. X-axis guide 15. Imaging Unit W....Object being measured (workpiece)

Claims

1. An interferometer optical head is used to acquire interference fringe images generated by the optical path difference of the light reflected from each of the following sources: an incoherent light emitted from a light source is split by a beam splitter into reference light for a reference mirror and measurement light for the surface to be measured. In a measurement method in which the interferometer optical head is scanned with respect to the surface to be measured from a starting point to an ending point in the Z-axis direction along the optical axis of the interferometer optical head, N (where N≧2) interference fringe images are acquired, and the surface shape of the surface to be measured is measured based on the N interference fringe images, Regarding the common position in the N interference fringe images, For an interference signal consisting of N point values ​​indicating the change in interference light intensity along the Z-axis direction, the phase φ of the interference fringes created by light of a predetermined analysis wavelength Λ is determined, and based on this phase φ, the relative position Z in the Z-axis direction of the measurement target surface within the range of the analysis wavelength is determined. ＦΛ Identify, Let z_p be the scan pitch in the Z-axis direction, and the nth data point be the number of data points counted from the starting point. The Fourier transform F(Λ-1) of the interference signal f(z) at the analysis wavelength Λ is obtained based on equation (2). [Math 1] A method for measuring surface shape to determine the phase φ of interference fringes produced by light of the analytical wavelength Λ based on the argument angle of F(Λ - 1) obtained as a complex number, After obtaining the first interference fringe image, While sequentially acquiring the M-th (where 2 ≤ M ≤ N) interference fringe image, analysis processing is performed on the interference fringe images up to M-1. After obtaining the Nth interference fringe image, the analysis process is performed on the first to Nth interference fringe images. The analysis process, at least for each position in the last acquired K-th interference fringe image, Equation (3) is calculated, [Math 2] By adding this to equation (4), which is the discrete sum of the Fourier transforms F(Λ-1) calculated for the first K-1 points, [Math 3] Equation (5) is the discrete sum of the Fourier transforms F(Λ - 1) at the analytical wavelength Λ for the first K points. [Math 4] This includes a Fourier transform process to calculate the result, The discrete sum obtained in the Fourier transform process in the analysis process performed after acquiring the Nth interference fringe image is defined as the Fourier transform F(Λ - 1) of the interference signal f(z) at the analysis wavelength Λ. A method for measuring surface shape, characterized by the following features.

2. The relative position Z in the Z-axis direction of the surface to be measured ＦΛ Equation (1) [Math 5] The measurement method according to claim 1, characterized by being calculated by the method described above.

3. Let ξ be an integer, then Λ = N·z ｐ Select ξ and Λ such that / ξ, and then perform the discrete Fourier transform F(Λ －１ The measurement method according to claim 1 or 2, characterized by determining the following:

4. The absolute position Z in the Z-axis direction of the measurement target surface ｓ is expressed as Z ｓ = Λ × m + Z ＦΛ where m is an integer, and the integer m is obtained by a method different from the calculation of the relative position Z ＦΛ of the Z-axis direction position Z of the measurement target surface. The integer m is specified based on Z Ｒ and the absolute position Z ｓ is calculated by = Λ × m + Z ＦΛ . The measurement method according to any one of claims 1 to 3, characterized in that ｓ the absolute position Z is calculated.

5. m (Z Ｒ -Z ＦΛ The measurement method according to claim 4, characterized in that it is the integer closest to ) / Λ.

6. The aforementioned analytical wavelength Λ is k × 2 ｎ (However, k is an integer multiple of 2 or more and is the scan pitch z) ｐ The measurement method according to claim 5, characterized in that the values ​​are selected to be such that the value is (a value that results in).

7. From the integral curve consisting of N points obtained by integrating the square or absolute value of the interference signal, a starting-side noise line approximating the starting-side noise region, which is the range where no interference occurs on the starting-side side of the measurement target surface, an ending-side noise line approximating the ending-side noise region, which is the range where no interference occurs on the ending-side side of the measurement target surface, and an interference line approximating the interference region, which is the range where interference occurs in the vicinity of the measurement target surface, are obtained. Based on the starting noise line, the ending noise line, and the interference line, the Z-axis position of the surface to be measured is determined. Ｒ A measurement method according to any one of claims 4 to 6, characterized by determining [the value].

8. The measurement method according to any one of claims 1 to 7, characterized in that the analysis wavelength Λ is selected from the vicinity of the wavelength at which the signal intensity is maximum when light irradiated from the light source is received by a photodetector for capturing the interference fringe image.

9. The measurement method according to any one of claims 1 to 8, characterized in that the analysis wavelength Λ is 290 nm or more and 350 nm or less.

10. The measurement method according to claim 9, characterized in that the analysis wavelength Λ is 320 nm.

11. A surface shape measuring device for measuring the surface shape of an object to be measured, An interferometer optical head that splits light emitted from a light source emitting incoherent light into reference light for a reference mirror and measurement light for the surface to be measured using a beam splitter, and acquires interference fringe images generated by the optical path difference of the light reflected from each using an image sensor, Analysis means for determining the surface shape of the surface to be measured based on the interference fringe image acquired by the interferometer optical head. Equipped with, The interferometer optical head acquires N interference fringe images (where N≧2) by scanning the surface to be measured in the Z-axis direction along the optical axis of the interferometer optical head from a starting point to an ending point. The aforementioned analysis means is For the common position in the N interference fringe images acquired by the interferometer optical head, the phase of the interference fringe created by light of a predetermined analysis wavelength Λ is determined from the interference signal consisting of N points representing the change in interference light intensity along the Z axis direction, and based on this phase, the relative position Z in the Z axis direction of the measurement target surface within the range of the analysis wavelength is determined. ＦΛ Identify, Let z_p be the scan pitch in the Z-axis direction, and the nth data point be the number of data points counted from the starting point. The Fourier transform F(Λ-1) of the interference signal f(z) at the analysis wavelength Λ is obtained based on equation (2). [Math 6] Based on the argument angle of F(Λ - 1) obtained as a complex number, we determine the phase φ of the interference fringes produced by light of the analytical wavelength Λ. A surface shape measuring device, The aforementioned analysis means is After the image sensor acquires the first interference fringe image, While sequentially acquiring the M-th (where 2 ≤ M ≤ N) interference fringe images using the aforementioned image sensor, analysis processing is performed on the interference fringe images up to the M-1th image. After acquiring the Nth interference fringe image using the image sensor, the analysis process is performed on the first to Nth interference fringe images. The analysis process by the analysis means includes, at least, each position in the K-th last acquired interference fringe image: Equation (3) is calculated, [Number 7] By adding this to equation (4), which is the discrete sum of the Fourier transforms F(Λ-1) calculated for the first K-1 points, [Number 8] Equation (5) is the discrete sum of the Fourier transforms F(Λ - 1) at the analytical wavelength Λ for the first K points. [Number 9] This includes a Fourier transform process to calculate the result, The surface shape measuring device is characterized in that the discrete sum obtained in the Fourier transform process in the analysis process performed after acquiring the Nth interference fringe image is the Fourier transform F(Λ - 1) of the interference signal f(z) at the analysis wavelength Λ.

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