JP5595463B2 - Wavefront optical measuring device - Google Patents

Description

  The present invention relates to an optical measurement device, and more particularly to a wavefront measurement device.

  Wavefront measurements are used to inspect the quality of optical surfaces and to evaluate the optical performance of optical elements. Wavefront measurement is also used for alignment of high-precision optical systems. The wavefront is the trajectory of a point where all the rays have the same phase (line or surface in the propagation of a three-dimensional wave). The simplest form of wavefront is a plane wavefront, where the rays are parallel to each other and a flat wavefront strikes the sensor. In wavefront propagation through optical elements such as lenses and mirrors, the wavefront shape generally changes due to lens thickness, surface shape imperfections, refractive index variations, and other factors. These changes in wavefront shape are known as aberrations. Therefore, knowing the wavefront profile and correcting the wavefront aberration is extremely important when designing an optical element and evaluating the performance of a newly designed optical system. For example, before assembling a complete imaging system, it is necessary to check the performance of each optical unit (unit lens) included in the system. Since the unit lens or the single lens itself may have some kind of aberration, it is necessary to control the quality of the image by the imaging lens with high accuracy.

  A conventional method for measuring the wavefront quality of a light beam uses an interferometric wavefront sensor. In an interferometric wavefront sensor, a spherical reference wave is generated by spatially filtering a small portion of the source beam, which is then combined with the original wavefront to generate an interferogram. As recognized in the art, the interferogram interference fringes can be analyzed to assess the quality of the light beam. However, splitting the original beam and recombining it with the reference beam tends to cause system aberrations such as optical path errors and improper alignment. Another conventional wavefront measurement method uses a Shack-Hartmann wavefront sensor that does not require splitting and recombining the original beam.

  The Shack-Hartmann wavefront sensor (SHWFS) is usually used as a wavefront sensor with a wide dynamic range. One of the most basic and commonly used configurations of SHWFS sensors consists of a lenslet array and a photodetector (typically a CCD camera). The Shack-Hartmann wavefront sensor divides the wavefront of the incident beam to be measured into a plurality of small beams by using a two-dimensional lenslet array. Each lenslet of the lenslet array produces a separate and independent focus (spot) on the surface of the photodetector. The position of the center of gravity of each spot is displaced by wavefront aberration that is the difference between the reference beam and the distorted beam. Therefore, wavefront measurement with a SHWFS sensor is based on measuring the local gradient of the wavefront including aberrations relative to the reference (planar) wavefront. In general, the wavefront estimation procedure depends on whether the phase is expressed as a number of local gradients of the wavefront or as a coefficient of some modal function determined over the entire aperture. It can be classified into either of these. In the latter case, the focal spot displacement may be expressed in the form of a Zernike polynomial. SHWFS has several advantages over interferometric wavefront sensors: SHWFS has a wider dynamic range than the interference measurement sensor. Incident radiation may not be coherent. Since SHWFS can acquire all of the wavefront information from a single image, the exposure time can be shortened and is therefore less susceptible to vibrations. More importantly, SHWFS provides both irradiance distribution and phase distribution.

  FIG. 1 shows a configuration example of a wavefront measurement system using SHWFS. In FIG. 1, a laser 1000, an ND filter 1001, a beam expander 1002, a lens 1004, an inspection optical element (that is, a sample) 1005, a lens 1006, a lens 1007, a lenslet array (microlens array) 1008, a CCD sensor 1010, data analysis. Part 1009 is arranged in a predetermined manner to characterize the effect of the sample on the wavefront of light passing through it.

  FIG. 2 shows the optical configuration of SHWFS in more detail. In FIG. 2, the location of the focal spot (2500-2503) on the detector array 2010 is determined by the local slope of the incident wavefront. The local inclination of the wavefront is caused by the aberration caused by the inspection optical element 1005 in FIG. This local tilt can be calculated by changing the location of the focal spot. By using local tilt information obtained from each lenslet of the lenslet array 1008, the wavefront can be reconstructed.

  If the deviation amount of the wavefront is narrower than the dynamic range of SHWFS, the position of each spot on the detector array 2010 can be detected separately. If the wavefront deviation exceeds the SHWFS dynamic range and the focal spots on the detector array 2010 overlap each other, the SHWFS can no longer analyze the wavefront. FIG. 3 shows a situation where the wavefront deviation exceeds the dynamic range of SHWFS. In FIG. 3, the focal spot 3500 is located outside the detector array 2010, and the focal spots 3501, 3502, and 3503 are located on the surface of the detector array 2010. However, the focal spots 3502 and 3503 intersect (ie, the beams that form these spots overlap each other and then focus on their respective locations after they intersect). This situation occurs when a wavefront including large aberrations enters the lenslet array 1008.

  FIG. 4A shows output data from the detector array 2010 in a state where the wavefront aberration is large. The focal spot in the outer region (shown by a square 4000) in FIG. 4 (a) is magnified in FIG. 4 (b) to better illustrate the adverse effects of wavefronts containing large aberrations incident on this outer region.

Certain techniques for expanding the dynamic range of SHWFS are available and are listed below.
(1) Null lens A null lens can partially compensate for the wavefront aberration of the inspection optical element, thereby reducing the wavefront deviation on the lenslet array. However, it may be necessary to produce a very accurate null lens in order to make an accurate measurement. Therefore, the production cost of the null lens is tremendously high. Further, since such a null lens is designed for a particular inspection optical element, this technique may not be applicable to other wavefronts formed by other inspection optical elements. An example of null lens technology is described in US Pat. No. 5,233,174 to Zmek. This patent is incorporated herein by reference.
(2) Estimation technology A wavefront estimation technology for measuring a wavefront including large aberration has been proposed instead of the null lens technology. An example of estimation techniques, reference 1 (Michael C. Roggemann, Timothy J. Schulz, Chee W. Ngai, and Jason T. Kraft, "Joint processing of Hartmann sensor and conventional image measurements to estimate large aberrations: theory and experimental results Appl. Opt. 38, pp. 2249-2255 (1999)). Reference literature 1 discloses an aberration estimation technique for enlarging the magnitude of aberration so that the Hartmann sensor can detect it. This technique uses an algorithm that processes both Hartmann sensor images and conventional images formed with the same aberrations. This technique is said to be able to accurately detect large defocus aberrations.

  Other estimation techniques include reference 2 (Harrison H. Barrett, Christopher Dainty, David Lara, “Maximum-likelihood methods in wavefront sensing. 391-414 (2007)), the wavefront is reconstructed using Maximum Likelihood Estimate (MLE). Although reference 2 describes that this technique can reduce residual wavefront errors, MLE technology requires attention to any noise sources and any factors that affect sensor data.

  One of the obstacles faced by the inventors of the present invention is that the quality of the image by the imaging lens needs to be controlled with high precision. Specifically, before assembling an imaging system that can be composed of a plurality of lenses, it is necessary to check the performance of each lens or lens group (unit lens). Even when the aberration of the imaging system is not so large, the aberration of each lens group (unit lens) or single lens may be large. Therefore, it is important to measure the aberration of the unit lens with such a large aberration.

  The estimation technique described above requires iterative calculation of optical forward propagation. The propagation model of Reference 1 is an angular spectrum propagation method based on Fourier optics. According to Fourier optics, the propagation of the light field can be calculated from surface to surface, and each surface can be a plane or a sphere, respectively. As shown in FIG. 5, assuming a simplified optical configuration, the inspection lens 5010 is illuminated by a point light source 5000. Light rays that pass through the inspection lens 5010 travel through the lenslet array 5020 and the wavefronts of these rays are detected by the CCD image sensor 5030.

  In propagation calculation based on Fourier optics, the configuration shown in FIG. 6 is typically assumed. In FIG. 6, an exit pupil 6010 (representing inspection optical element 5010 of FIG. 5) is established on surface P1, lenslet array surface 6020 is placed on surface P2 instead of lenslet array 5020, and detector array surface 6030 is The detection surface of the CCD image sensor 5030 in the plane P3 is represented. However, the simplified “surface” representation of FIG. 6 is inaccurate because the actual lenslet array 5020 is formed on a substrate having some thickness, and each lenslet also has some thickness. .

  Accordingly, assuming an ideal thin surface as the lenslet array surface 6020, the accuracy of the propagation calculation may be impaired. In particular, when the light in the lenslet array 5020 converges or diverges, large spherical aberration is caused by the lenslet substrate, and coma and astigmatism are caused by the lenslet. Therefore, it may be difficult to incorporate (compensate) the effects of these aberrations into the propagation based on Fourier optics. Furthermore, it may be difficult to consider the effects of optical component misalignment in methods based on Fourier optics.

  Further, in the propagation model of Fourier optics, the dynamic range of the wavefront to be measured is restricted by the number of samplings required to satisfy the sampling theorem in the Fourier domain. As an example, in the configuration of FIG. 5, the distance between the point light source 5000 and the inspection lens 5010 is 127.5 mm, and the wavefront deviation on the exit pupil spherical surface is represented by the Zernike coefficient shown in FIG.

  In order to calculate the forward propagation model with the optical element based on the Fourier optics as the inspection arrangement shown in FIG. 5, the configuration by the Fourier plane shown in FIG. 6 can be assumed. Specifically, as described above with reference to FIG. 6, the inspection lens 5010 of FIG. 5 is represented by the exit pupil plane 6010 (the surface of the dummy surface) on the plane P1. FIG. 8 shows a wavefront deviation on the exit pupil plane 6010 (wavefront on the surface of the dummy surface) in FIG.

  In this case, the number of samplings on the exit pupil plane 6010 requires about 14300 samples over the entire pupil plane in order to satisfy the sampling theorem in the outermost contour region of the pupil. Propagation based on FFT (Fast Fourier Transform), such as angular spectrum propagation, typically requires more samples than this number. Therefore, even with the simplified configuration of FIG. 5, the number of samplings required for two-dimensional propagation in the method based on Fourier optics can be approximately 30000 × 30000.

  FIG. 9 shows an estimated calculation time required for one FFT calculation using a processing unit (data analysis unit) including an AM + Phenom 9950 CPU manufactured by AMD. When performing FFT on 30000 × 30000 samples, such a memory size is very large for workstations currently on the market. If this data size can be manipulated, the time required for one FFT calculation is about 65 seconds. Since angular spectrum propagation requires two sets of FFT calculations, one angular spectrum propagation takes at least 130 seconds. In the estimation procedure, the forward model is iteratively calculated. If several parameters are estimated simultaneously, the total time for wavefront estimation becomes unrealistically long. As the wavefront deviation increases, much longer computation time and more memory are required.

  Therefore, the propagation calculation technique based on Fourier optics requires a complicated model for propagation calculation and enormous computational resources. As a result, this technique can be used only for estimation of a small number of parameters in practice with many restrictions on modeling of the propagation model.

US Pat. No. 5,233,174

Michael C.M. Roggemann, Timothy J. et al. Schulz, Chee W. Ngai, and Jason T. Kraft, “Joint processing of Hartmann sensor and conventional image measurements to estimate large abrasions: theory and experimental results.” Opt. 38, 2249-2255 (1999) Harrison H. Barrett, Christopher Dainty, and David Lara, “Maximum-likelihood methods in wavefront sensing: stochastic models and likehood func. Opt. Soc. Am. A. 24, 391-414 (2007) Jae Myung, “Tutorial on Maximum Likelihood Estimation”, Journal of Mathematical Psychology, 47, 90-100 (2003) B. D. Stone, T.M. J. et al. Bruegge, “Practical conjugations for simulative beam propagation: A comparison of three approaches”, Proc. SPIE 4832, 359-378, (2002)

According to one aspect of the present invention, an apparatus for measuring the wavefront of light passing through an inspection optical element acquires a light intensity, a lenslet array through which light from the light source passes, and a light intensity distribution via the lenslet array. A detector array configured to, and a processing unit, wherein the processing unit performs data processing using the acquired light intensity distribution, the data processing being based on a beamlet based propagation model or ray Includes an estimation process that uses the propagation model as the forward propagation model.

  Further features of the present invention will become apparent from the following description of exemplary embodiments, taken in conjunction with the accompanying drawings.

It is a figure which shows the optical structure of the wavefront measuring system using a Shack-Hartmann wavefront sensor. It is a figure which shows the optical structure of SHWFS. It is a figure which shows the focal spot of a state with a large aberration. It is a figure which shows the output data from a detector array. It is a figure which shows the optical structure of a wavefront measurement. It is a figure which shows the optical structure for propagation based on Fourier optics. It is a figure which shows the Zernike coefficient showing the wavefront deviation in an exit pupil spherical surface. It is a figure which shows the wave front in the surface of a dummy surface. It is a figure which shows the calculation time required for one FFT calculation. It is a figure which shows the structure of a measurement system. It is a figure which shows the schematic of a data analysis part. It is a figure which shows the optical structure for forward propagation which has an exit pupil plane. It is a figure which shows the optical structure for front models which have an exit pupil spherical surface. It is a figure which shows the density of the beamlet on a lenslet , and intensity distribution on an image sensor surface. It is a figure which shows the density of the beamlet on a lenslet , and intensity distribution on an image sensor surface. It is a figure which shows the optical structure for front models. It is a figure which shows the optical structure of the wavefront measurement of a lens unit. It is a figure which shows a cost function profile. It is a figure which shows a detector output image. It is a figure which shows the dependence with respect to the image sensor pixel number of calculation time. It is a figure which shows the dependence with respect to the Zernike coefficient of the cost function in a front model. It is a figure which shows the schematic of the data analysis part using a database. It is a figure which shows the example of a detector output image. It is a figure which shows the relationship between the cross section of an image, and an intensity | strength peak position. It is a figure which shows the forward calculation model based on light optics. It is a figure which shows the change of the position of the image produced | generated on a detector when a lens unit has a manufacture error. It is a figure which shows the model provided with the dummy element (or dummy surface) inserted as a part of optical system. It is a figure which shows the change of the cost function with respect to the number of iterations. It is a figure which shows the optical structure which defines two or more light rays for every lenslet. It is a figure which shows the case where one light ray or beamlet is traced through each lenslet. It is a figure which shows the case where two or more rays or beamlets are tracked through each lenslet. It is a figure which shows the case where two or more rays or beamlets are tracked through each lenslet.

Exemplary embodiments of the invention are described below.
(First embodiment)
The first embodiment of the present invention is directed to a solution to the problem described above. FIG. 10 shows a configuration of a wavefront optical measuring apparatus according to the present invention.

  In FIG. 10, the light source 1100 emits a light beam that is shaped by the illumination optical element 1102 after passing through the ND filter 1101 (if present). Next, the shaped beam illuminates the inspection optical element 1103 such as a lens. This light beam passes through the inspection optical element 1103 and the lenslet array 1104, and then the detector array 1105 detects the light distribution generated by this optical system.

  The detector array 1105 outputs a signal having information about all of this optical system. The data analysis unit 1106 can use the MLE method, and analyzes various optical parameters related to this optical system including the inspection optical element 1103.

  As the light source 1100, a coherent light source such as a pulse laser or a continuous wave (CW) laser, or a non-coherent light source such as a mercury lamp or a tungsten lamp may be used. In the case of a CW laser or lamp, a modulation device such as an optical chopper may be required to modulate the light beam. Illumination optics that shape the light beam are considered well known to those skilled in the art and will not be described herein. As lenslet array 1104, various lenslet arrays (one-dimensional and two-dimensional) are readily available from commercial suppliers well known in the art. Certain parameters such as the shape, pitch, and focal length of the lenslets in the array are generally dependent on the particular application of the measurement device. Similarly, the detector array 1105 can be implemented as a single CCD camera, as is well known in the art. Alternatively, the detector array 1105 can be implemented as a one-dimensional or two-dimensional CMOS sensor array that can be specifically designed using, for example, large scale integration (VLSI) electronics.

  FIG. 11 shows a schematic diagram of the data analysis unit 1106. The data analysis unit includes a calibration module 1107 and a parameter estimation module 1108. The data analyzer may be implemented as a programmable computer or data processing unit that may be specifically configured to execute the process sequence of steps S11-S18. The data analysis unit and its constituent modules can also be implemented as individual hardware elements or distributed processing units. In the present embodiment, the data analysis unit 1106 may be implemented as a programmable computer including a data processing unit such as the AM + Phenom 9950 CPU manufactured by AMD described above.

  During operation of the data analysis unit 1106 of FIG. 1, the lenslet parameters and the measured illumination distribution are input manually or automatically at step S11. The lenslet parameters may include optical information such as the focal length and pitch of the lenslet array, the number of lenslets in the lenslet array. The measured illumination distribution can be obtained from the detector array 1105 via the data acquisition system 1120, or can be pre-stored measurements from a local or remote storage device (not shown) (eg, current (Measurement illumination distribution). The lenslet parameters and illumination distribution thus input are provided to the calibration module 1107. Some of the functions of the calibration module 1107 may be to obtain information about the positional relationship between the lenslet array and the detector array, or to properly align (calibrate) the positions of these two arrays. That is, as described further below, the calibration module 1107 may be used to interactively align the actual optical unit via a feedback circuit. Additionally or alternatively, a calibration module can be used to obtain the positional relationship between the optical units as information (data) that can be used as input information for the estimation process. To that end, in step S12, the positions of the lenslet array and other optical elements are defined using reference data obtained without the inspection optical element 1103. That is, in step S12, the reference data is measured without using the inspection lens (inspection optical element 1103) in the optical apparatus of FIG. Thereby, the detector array 1105 detects a substantially plane wave profile as shown in the screen shot 1121. The data acquisition system 1120 provides this reference data to the calibration module 1107 of the data analysis unit 1106. Thereby, in step S12, the initial optical configuration of the measuring apparatus including the position of the lenslet array is set. Once the initial optical configuration is set by the calibration module 1107, the flow process proceeds to the sequence steps performed by the parameter estimation module 1108.

When reference data is acquired by the data analysis unit 1106 and the initial optical configuration of the measurement apparatus is established, the inspection optical element 1103 is positioned and measurement is performed. In step S 13, an initial parameter describing the wavefront formed by the inspection optical element 1103 is set in the parameter estimation module 1108. Specifically, the initial parameter is set as a Zernike coefficient that can be zero as a default value. In other words, in step S13, the parameter estimation module 1108 sets an initial parameter that can represent a substantially plane wave (Zernike coefficient value is zero). When steps S11 to S13 are completed, a forward model is calculated in step S14 based on the value received from at least one of steps S11 to S12 and the initial parameters set in step S13. That is, in step S14, the forward propagation model changes the initial parameters set in step S13 based on the reference data obtained without the inspection optical element, the optical configuration of the measuring apparatus, and the data of the inspection optical element. Calculated by As discussed in more detail below, a beamlet based propagation model or a ray based propagation model may be used as the forward propagation model. When the forward model (simulation data) is established, the process proceeds to step S15. In step S <b> 15, the data acquisition system 1120 acquires actual experimental data from the detector array 1105. Specifically, in step S15, actual experimental data is measured using an inspection lens (inspection optical element 1103) in the optical apparatus of FIG. Thereby, as shown in the screen shot 1122 of FIG. 11, the detector array 1105 detects the wavefront profile formed by the inspection optical element 1103. The data acquisition system 1120 provides the actual experimental data (measurement data) to the parameter estimation module 1108 of the data analysis unit 1106.

  In step S15, the data analysis unit 1106 is obtained by using actual experimental data that is actually measured data (for example, the one shown in the screen shot 1122 of the data acquisition system 1120) and the forward model in step S14. The likelihood of the difference from the simulated data is calculated. The likelihood of difference can indicate how small the difference between actual experimental data and simulation data can be. Here, the likelihood may be based on an estimation algorithm (discussed below) that can determine whether actual experimental data and simulation data can converge. Therefore, in step S16, it is inspected whether actual experimental data and simulation data are converged. That is, in step S16, it is examined whether the Zernike parameters of the front model converge on the same parameter representing the wavefront profile. If the calculation result converges in step S16, the estimated parameter (the parameter established by the forward model) is output. However, if the calculation result does not converge, the estimated parameters can be changed in step S18, and the steps between S14 and S16 are iteratively repeated until this result converges. When the difference between the actual experimental data and the simulation data obtained by using the estimated parameters is equal to or less than the threshold value, the calculation result may be converged.

  The calibration module 1107 of the data analysis unit 1106 allows the analysis unit to calibrate some optical parameters such as optical element position, detector parameters, and illumination distribution. Specifically, once the lens parameters and the measured illumination distribution are input in step S11, the calibration module 1107 calibrates the optical system by known electronic techniques so that the desired parameters are established therein. To do. For example, the calibration module 1107 may send an electronic signal to illuminate the light source 1100 with sufficient output to obtain the desired illumination distribution at the detector 1105. Further, the calibration module 1107 may output an electronic signal indicative of at least one desired position of the inspection optics 1103, the lenslet array 1104, and the detector 1105. In response to a calibration signal output from calibration module 1107, inspection optics 1103, lenslet array 1104, or detector 1105 are each moved (or aligned) to a desired position and optimal at detector 1105. An illumination distribution is obtained.

  The parameter estimation module 1108 performs an estimation function that estimates the optical parameter of interest when the inspection optical element 1103 is present in the optical system. These parameters may include the position of each optical element including inspection optical element 1103 as well as the wavefront deviation or intensity distribution in a particular plane or sphere of inspection optical element 1103.

  This estimation procedure may use maximum likelihood estimation (MLE) techniques. Descriptions of MLE are described in Reference 3 (Jae Myung, “Tutorial on Maximum Likelihood Estimation”, Journal of Mathematical Psychology, 47, 90-100 (2003)) and Reference 2.

  The probability distribution function (PDF) is indicated by pr (g | θ). Here, g is an observation data vector characterized by an M × 1 vector, and θ is a parameter vector characterized by a P × 1 vector. The likelihood of θ is expressed by equation (1).

... (1)
The maximum likelihood (ML) estimate of θ is defined by equation (2).

... (2)
In practice, it may not be possible to analytically obtain an ML estimate, so that the ML estimate is determined numerically. For example, when the PDF is defined by a Gaussian distribution, the likelihood is derived as Expression (3).

... (3)
Where
Is the average value of the data, calculated by the forward model. σ ² is a variance value of noise. The log likelihood can be described as equation (4).

... (4)
As a result, the ML estimated value is described as Equation (5).

... (5)
In the parameter estimation process described in FIG. 11, the ML estimate is calculated iteratively. Data for ML estimate calculation

Is necessary. data

Is calculated in the “calculate forward model” step, and then the ML estimate lnL (θ | g) is calculated in the “calculate likelihood” step. ML estimate

Is obtained by an optimization search method.

  As mentioned above, forward model computation may be used in the MLE for this measurement system. In this forward model, it is necessary to calculate the detector output signal, for which light propagation calculations are performed. The most common method is FFT-based propagation. This method is based on Fourier optics, such as Fresnel diffraction and angular spectral propagation.

  However, such FFT-based propagation has the problems described above. The method based on FFT requires an unrealistically large number of samplings and a long calculation time for propagation of a wavefront including large aberrations.

To overcome these problems, at least one embodiment of the present invention uses beamlet based propagation instead of FFT (Fast Fourier Transform) based propagation such as angular spectral propagation. Furthermore, in order to minimize processing time and optimize accuracy, other embodiments disclose a combination of ray-based propagation and beamlet- based propagation.

References 4 (B D. Stone, T J. Bruegge,... , "Practical considerations for simulating beam propagation: A comparison of three approaches ", Proc SPIE 4832,359~378, (2002) ) based on the beamlet propagation Is described. Reference 4 describes the decomposition of a Gaussian beam as propagation based on beamlets .

As an example of propagation based on beamlets , the optical configuration will be described with reference to FIGS.

  FIG. 12 shows an optical configuration for forward propagation using the exit pupil plane 2200, and FIG. 13 shows an optical configuration for the front model using the exit pupil spherical surface 2300. In FIG. 12, 2205 and 2210 (2305 and 2310 in FIG. 13) represent a lenslet array and a CCD (Charge Coupled Device) image sensor, respectively. Define a wavefront or complex amplitude distribution in the plane or sphere of the exit pupil, respectively. Ray tracing is performed from a light source (not shown) to the CCD image sensor surface. The location and direction of the ray is calculated based on the wavefront at the pupil and other optical design parameters.

In propagation based on beamlets , each ray is a thin beamlet such as a Gaussian beam distribution. Multiple beamlets can be superimposed on the image sensor surface and then the intensity profile at the image surface can be calculated.

If there is no lenslet array in the optical system, the number of beamlets is determined based on the size of the exit pupil plane, and this method (ie propagation based on beamlets ) can be a very efficient propagation method.

However, if there is a lenslet array 2205 (2305) in the optical system as described in FIG. 12 or 13, it in the present invention, the density of beamlets within each lenslet is based on the beamlet propagation It was found to be a major factor in maintaining the accuracy of.

14 (a)-(e) and FIGS. 15 (a)-(d) above disclose the density or number of beamlets 2452 on the lenslet array 2450. FIG. 14A to 14E disclose the light intensity distribution (light spot) on the image sensor surface 2210 (2310). This light intensity distribution is obtained by using propagation based on beamlets . In the calculation shown in the figure, beam synthesis propagation (BSP) provided in “code V (registered trademark)” was used. code V® is a commercial software package developed by Optical Research Associates. As shown in FIGS. 14A to 14E, the number of beamlets 2452 per lenslet 2450 is 0 or 1, 1, 1 or 2, 1 to 3, and 1 to 4, respectively.

As described above, when there is no lenslet array in the optical system, the number of beamlets is determined based on the size of the exit pupil. However, when the optical system includes a lenslet array, it may be difficult to determine the number of beamlets based on the size of the exit pupil. The size of each lenslet in the lenslet array is much smaller than the size of the exit pupil, so if the number of beamlets is determined based on the exit pupil size and taking into account the calculation time and accuracy, The number is too small to represent.

Finally, if the lenslet array is present in the optical system, the number of beamlets should decide based on the number of lenslets in lenslet array, if so, contribution image sensor from every lenslet It is expressed correctly in the light intensity distribution (light spot) on the surface.

As described in FIGS. 14A to 14E, the spot image is determined by the number of beamlets for each lenslet . Further, as described with reference to FIGS. 15A to 15D, when using at least three beamlets per lenslet , it may be preferable to obtain an ideal spot image.

When the beamlet density is 3 or more per lenslet ( beamlet / lenslet ratio), propagation based on this beamlet can calculate a more appropriate spot array image on the image sensor surface.

  The data analyzer can then estimate the optical parameters of interest of the component of the optical system or with a simple optical system. Therefore, according to at least one embodiment of the present invention, it is possible to accurately measure a wavefront including large aberrations, which is difficult to measure with conventional measurement techniques.

As a result, the optical performance of a single lens, a lens unit, or a plurality of optical components can be verified using a simple optical configuration.
(Second Embodiment)
As previously mentioned, instead of angular spectral propagation, propagation based on beamlets can be used to measure wavefronts with large aberrations. The amount of wavefront aberration can be determined based on the amount of wavefront deviation. Specifically, in the beamlet- based propagation method, each beamlet forms a separate focal point (spot), and the center of gravity of each spot is displaced by wavefront aberration, so the deviation of each displaced spot is wavefront distortion. Corresponding to Thus, the total beam wavefront distortion can be reconstructed by integrating the deviations of each wavefront. If the wavefront has a very large deviation on the pupil (such as hundreds or thousands of wavelengths), a relatively large number of beamlets may be required to represent this deviation.

However, since the number of beamlets is limited by computational resources, the accuracy of propagation based on beamlets decreases rapidly when the amount of wavefront deviation exceeds a certain level.

  FIG. 16 is a diagram for explaining a forward model that can solve this problem. In FIG. 16, 2500, 2504, 2505, and 2506 represent the surface of the dummy surface, the inspection optical element, the lenslet array, and the CCD image sensor, respectively. This front model has lens data and a dummy surface 2500. When the lens design data of the inspection optical element 2504 is defined in this model, the wavefront deviation on the dummy surface 2500 is much smaller than the wavefront deviation on the dummy surface without using the lens design data. Using this forward model, the wavefront deviation or lens design parameters are estimated in the data analysis unit.

  Wavefront aberration can be converted using these estimation results. In addition, any optical parameter of interest can be measured. FIG. 17 shows an optical configuration for measuring the lens unit 2608 (lens group). Reference numerals 2600, 2608, 2609, 2610, and 2615 denote a point light source, an inspection lens unit, a dummy surface, a lenslet array, and a CCD image sensor, respectively. In this case, optical parameters such as a surface profile, lens thickness, inter-lens distance, misalignment, inclination, or refractive index distribution can be set as estimation targets estimated by the data analysis unit.

  The wavefront measurement data is expressed using a Fringe Zernike polynomial. Table 1 shows these polynomials. In this case, the coefficient of each polynomial is the measurement target. The detector output from the CCD image sensor is acquired by the optical system shown in FIG. The wavefront deviation expressed using the Fringe Zernike polynomial is defined on the dummy surface 2609 in the forward model shown in FIG. Next, the data analysis unit searches for a fringe Zernike coefficient that maximizes the log likelihood function.

  FIG. 18 shows a graph of the normalized cost function profile calculated using the detector output data calculated by simulation. The cost function is related to the square of the difference between the experimental data and the calculated data at each pixel of the detector. Assume that the number of pixels in the detector array is 1280 × 1024. The normalized cost function corresponds to the negation of the log likelihood function, and the Zernike coefficient that minimizes the cost function is the maximum likelihood value. In this example, the detector output data is generated under the condition that all the Zernike coefficients on the dummy surface are zero.

  Therefore, Zernike coefficient = 0 is an optimum value. As the Zernike coefficient changes, the normalized cost function also changes. In practice, the initial Zernike coefficients are unknown, so the estimation process searches for the minimum cost function in this profile.

  In the case of C37, which means the coefficient of the 37th Fringe Zernike polynomial, the average calculation time for calculating one cost function is measured as 50 seconds. Most of the calculation time is spent calculating the detector output data shown in FIGS. The numbers of pixels in FIGS. 19A to 19C are 1280 × 1024, 640 × 512, and 320 × 256, respectively. When the number of pixels of the output data can be reduced, the calculation time can also be shortened.

  FIG. 20 shows the dependence of the computation time for one forward model on the number of pixels in the detector array. If the number of pixels is reduced from 1280 × 1024 to 80 × 64, the computation time can be shortened from 50 seconds to 10 seconds. That is, since most of the measurement time is used for forward model calculation, the calculation time for the entire measurement including Zernike coefficient estimation can be reduced to 1/5. According to these results, the measurement time can be shortened by using a small number of pixels. On the other hand, in this case, the measurement accuracy is deteriorated. FIG. 21 shows the dependence of the cost function on the forward model on the Zernike coefficients for several different numbers of pixels in the detector array.

  The slope of the cost function profile when the number of pixels is 80 × 64 is smaller than the slope when the number of pixels is 1280 × 1024. This result means that the measurement sensitivity is low when the number of pixels is 80 × 64. However, the most important thing at the start of the estimation process is how fast the search point can move to the vicinity of the optimal point, so high sensitivity is not required. Therefore, an image with a small number of pixels can be applied to a rough search. Applying an 80 × 64 pixel image to 60% of the overall estimation process can reduce the computation time by 48% while maintaining the same measurement accuracy. In actual measurement systems, different pixel numbers may be applied depending on the computational resources and the required accuracy.

  For each measurement, a forward model is calculated in the data analysis part of the measurement system. In a single lens or lens unit production line, the optical performance of similar types of lenses or lens units having the same design parameters is measured. In this case, at the beginning of the estimation process, a forward model with similar parameters is repeatedly calculated in each measurement.

  FIG. 22 shows a schematic diagram of the data analysis unit of the measurement system including the database 1110 stored in the memory device (unit) 1109. The difference between the step of FIG. 11 and the step of FIG. 22 is step S304. Specifically, after step S13, there is a step S304 in which the database 1110 is searched to determine whether data exists in the database. If useful data exists in the database 1110, the likelihood is calculated in step S15 using this data. If such data does not exist in the database 1110 in step S304, step S14 can be executed, and the calculation result can be stored in the database.

  This database may store a plurality of previously calculated forward model output data. These forward model output data are stored with the calculation parameters defined in each forward model, and then this database is indexed. When the same or similar lens is measured by the optical measurement device, the parameter estimation process in the data analyzer searches the data calculated using the similar parameters in the indexed database. If similar data is found in the database, the likelihood is calculated using this data (in step S15). If no similar data is found, a new forward model is calculated and the calculated data is then stored in the database. While similar lenses are repeatedly measured, the database will have calculated data with similar parameters, thus reducing the number of forward calculations required.

  In other words, the measurement time can be shortened during repeated measurements. In the data of 1280 × 1024 pixels, the file access time is less than 0.5 seconds, and this time is 1/100 shorter than the time taken to calculate the forward model. Thus, the measurement system can be used to continuously accelerate the measurement.

  Furthermore, the data stored in the database can be calculated outside the measurement system. The forward model can be pre-calculated with various parameters by a computer not used in the office or server room. As a result, the processing in this measurement system can be continuously accelerated. This acceleration of likelihood calculation results in more iterations in the estimation process. As a result, the measurement accuracy can be continuously improved.

  In this system, different data with different numbers of pixels can be stored in the database. For coarse measurements, small pixel count data can be applied. In this case, the file access time can be shortened.

  In the above description, measurement using data of one detector array has been described, but a plurality of detector data can be applied. Acquiring multiple detector data at different detector positions, illumination modes, polarization states, or inspection lens positions contributes to improved measurement performance.

According to the present invention, it is possible to measure a wavefront including large aberration that could not be measured by a conventional measurement technique. Optical parameters can also be measured. As a result, the optical performance of the lens or lens unit can be verified using a simple optical configuration.
(Third embodiment)
In order to reduce the calculation time, the third embodiment describes a modeling and calculation method that can significantly reduce the time taken to estimate large wavefront aberration.

  FIG. 23 shows an example of a detector output image similar to FIG. Referring to FIG. 23, those skilled in the art should note that all spots within circle 2300 are defined by their intensity peak positions.

  FIG. 24 shows the relationship between the cross section of the image of FIG. 23 and the intensity peak position that can be observed on the detector.

  In such a case, the characteristics of the image can be analyzed based on light beam optics (geometric optics) without taking diffraction into account or without using BSP (beam synthesis propagation). In this case, it is possible to use ray optics (geometric optics) instead of using the BSP to calculate the forward model in the process shown in FIG. 11 of the first embodiment.

FIG. 25 shows an arrangement for a forward calculation model based on ray optics. A forward calculation based on the beamlet can also be performed using this model. Reference numeral 3500 denotes a point light source. The lens unit 3501 assumes that there is no manufacturing error by using the design data for the simulation. The lenslet array 3502 includes N lenslets 3504, where N is a positive integer greater than one. For the i th lenslet, the ray from the point source 3500 directed to the center of this lenslet can be traced. The intersection of this ray (i-th ray 3505 in FIG. 25) and a point at detector 3503 can then be calculated. This point represents the position of the spot image generated on the surface of the detector 3503 by the i-th lenslet, and is described as (x _i , y _i ). Suppose that only one ray is traced per lenslet, and a total of N rays are considered in a lenslet array consisting of N lenslets.

  When the lens unit 3501 has a manufacturing error, the position of the image generated on the detector 3503 is affected as shown in FIG. In this case, the intersection of the i-th light beam 3505 and the detector 3503 is

Is represented by The image distribution on detector 3503 is determined by these points.

Each can be obtained experimentally. Where i = 1, 2, 3. . . N. The influence of the manufacturing error can be evaluated using such experimental data, and finally the wavefront aberration of the lens unit is estimated using the parameter estimation module 1108 of the data analysis unit 1106 of FIG. 11 or FIG. Can do.

In the calculation, the model shown in FIG. 27 can be used. Here, a dummy element (or dummy surface) 3701 is inserted as a part of the optical system. The purpose of using the dummy surface is as described in the second embodiment with reference to FIGS. 16 and 17. If there is no manufacturing error, the dummy element 3701 does not affect the optical performance. If there is no manufacturing error, the i-th ray intersects the detector at (x _i , y _i ) as shown in FIG. If there is a manufacturing error, this point is as shown in FIG.
Sneak away. The influence of the manufacturing error is represented by a Zernike coefficient defined on the surface of the dummy element 3701.

In order to evaluate the influence of the manufacturing error of the lens unit and estimate the wavefront aberration of the lens unit,
Define the cost function, and then minimize the cost function by changing the Zernike coefficients in the dummy elements. This process is similar to the optimization calculations used in lens designs that minimize the cost function by iteration.

  FIG. 28 shows the change of the cost function with respect to the number of iterations. In this example, the results shown in Table 2 are obtained after three iterations for each Zernike coefficient.

In this optimization, Zernike coefficients (2 to 36, see Table 1 of the first embodiment) are set as variables. Their initial values are zero, and Table 2 shows optimized values that minimize the cost function. The number of rays (or the number of lenslets) used for estimation in this example was 1,245. The computation time required for the 3 iterations was about 15 seconds. This is much shorter than with beamlet based propagation modeling.

  One advantage of building a model based on ray optics is that the optimization process can be performed in the same way as a lens design applying a very advanced lens design algorithm.

  In the above example, only one ray per lenslet was considered, but in order to more accurately model the characteristics of each lenslet, two or more rays for each lenslet as shown in FIG. Can be defined. In FIG. 29, 3900, 3901, 3902, 3903, and 3904 represent a point light source, a dummy surface, a lens unit, a lenslet array, and a detector, respectively.

In the above modeling, a beamlet using BSP can be used instead of the light beam . In order to make full use of the experimental results, at least one beam or beamlet is required for each lenslet. When a single ray or beamlet is tracked through each lenslet, FIG. 30 shows the position of the ray or beamlet 4001 on the lenslet . In order to ensure the accuracy of the calculation, it is necessary to position this ray or beamlet at the center of (or near) the corresponding lenslet 4000.

31 and 32 show a case where a plurality of light beams or beamlets are traced through each lenslet. If tracking multiple rays or beamlets for each lenslet, to achieve a uniform light density (or beamlets density) in all directions, as shown in FIG. 32, the number of rays or beamlets Ideally Should be 3 or more.

Referring again to FIG. 23, the area outside the circle 2300 in FIG. 23 cannot be accurately modeled based on ray optics, but can be accurately modeled using propagation based on beamlets . In other words, according to at least one embodiment of the present invention, a ray-based propagation model may be used for regions of the wavefront where the aberration is less than some aberration level. On the other hand, a propagation model based on a beamlet can be used as a forward propagation model for a wavefront region having aberration above a predetermined level. This aberration level may be determined by the amount by which the Zernike coefficients are affected during the iterations of steps S14-S16 in the parameter estimation process described with reference to FIG. The determination of whether to use a ray-based propagation model or a beamlet- based propagation model is also based on whether the estimated parameters have converged, as described with reference to step S16 of FIG. Sometimes. Thus, according to at least one embodiment of the present invention, a ray-based propagation model or a beamlet- based propagation model can be selectively used as the forward propagation model based on the level of wavefront aberration. The advantage of ray-based modeling is its computational speed, and the advantage of beamlet- based modeling is its accuracy.

The two modeling methods can then be combined appropriately in implementing this wavefront estimation technique. For example, ray-based modeling can be used for coarse estimation, and then a more detailed estimation can be made based on beamlet- based modeling using the results of ray-based estimation. More specifically, ray-based propagation is used to quickly assess any possible impact that fabrication parameters can have on a given area of an optical component (eg, a central area or a flat area) and is based on beamlets . Propagation can be used to accurately determine (estimate) the amount of wavefront aberration in a more sensitive area (eg, the outer region) of the optical component being inspected.

  Although the invention has been described with reference to exemplary embodiments, it should be understood that the invention is not limited to the disclosed exemplary embodiments. The appended claims are to be accorded the broadest interpretation and thus all modifications and equivalent structures and functions are intended to be included.

DESCRIPTION OF SYMBOLS 1000 Laser 1001 ND filter 1002 Beam expander 1004, 1006, 1007 Lens 1005 Inspection optical element 1008 Lenslet array 1009 Data analysis part 1010 CCD sensor 1100 Light source 1101 ND filter 1102 Illumination optical element 1103 Inspection optical element 1104 Lenslet array 1105 Detector Array 1106 Data analysis unit 1107 Calibration module 1108 Parameter estimation module 1109 Memory device 1110 Database 1120 Data acquisition system 1121 Screenshot 1122 Screenshot 2010 Detector array 2200 Exit pupil plane 2205 Lenslet array 2210 Image sensor 2300 Exit pupil curved surface 2300 Circle 2305 Lens Let Array 231 0 The image sensor 2450 lenslet array 2452 beamlets 2500 dummy surface 2500-2503 focal spot 2504 inspection optical element 2505 lenslet array 2506 image sensor 2600 points source 2608 inspection lens unit 2609 dummy surface 2610 lenslet array 2615 CCD image sensor 3500 points source 3501 Lens unit 3502 Lenslet array 3500-3503 Focus spot 3503 Detector 3504 Lenslet 3505 Ray 3701 Dummy element 3900 Point light source 3901 Dummy surface 3902 Lens unit 3903 Lenslet array 3904 Detector 4000 Rectangular area 4000 Lenslet 4001 Ray or beamlet 5000 point light source 5010 inspection Lens 5020 lenslet array 5030 CCD image sensor 6010 exit pupil 6020 lenslet array surface 6030 detector array surface

Claims (9)

An apparatus for measuring the wavefront of light passing through an inspection optical element,
A light source;
A lenslet array including a plurality of lenslets through which light from the light source passes;
A detector array configured to obtain a light intensity distribution via the lenslet array;
A processing unit,
The processing unit performs data processing using the acquired light intensity distribution, and the data processing uses at least one of a beamlet-based propagation model and a ray-based propagation model as a forward propagation model. only including,
The optical configuration in the forward propagation model has a dummy surface, and is for estimating the shape of the wavefront on the dummy surface,
The estimation process optimizes the variables that define the dummy surface such that the difference between the light intensity distribution detected by the detector array and the calculated light intensity distribution on the surface of the detector array is reduced. Including estimating the shape of the wavefront on the dummy surface,
A device characterized by that.   The number of beamlets or rays passing through the inspection optical element is determined based on the forward propagation model used so that at least one ray or beamlet is assigned to each lenslet of the lenslet array. The apparatus of claim 1.   The apparatus according to claim 1, wherein the number of beamlets or light beams transmitted through the lenslets of the lenslet array is at least three in a beamlet-based propagation function or a light-based propagation function.   The apparatus of claim 1, wherein the processing unit includes a calibration function and a parameter estimation function for processing data output from the detector array to calculate the forward propagation model.   The apparatus of claim 1, further comprising a database for storing pre-calculated images on the detector.   The apparatus according to claim 1, further comprising a setting unit configured to set the number of pixels used for the data processing. 7. The apparatus according to claim 1, wherein a Zernike coefficient is used as the variable. The optimization is performed using a cost function including a square of a difference between a light intensity distribution detected by the detector array and a light intensity distribution on a surface of the detector array obtained by calculation. The apparatus according to any one of claims 1 to 7. The apparatus of claim 8, wherein the optimization is made to minimize the value of the cost function.