2.1

Light source L

A light source with very good imaging properties is required for the wavefront measurement. As light source, a broadband laser is proposed. There are two main disadvantages of a laser. One is a relatively high price, and the other is the higher noise and lower stability of the laser compared with, for example, a tungsten lamp. The visible stability is ± 0.5% in the range of milliseconds to seconds according to the manufacturer [9]. On the other hand, there are big advantages of a laser source. The most important ones are the high intensity and the good beam quality. With the high spectral power of the laser, the spectral bandwidth of the measuring beam can be reduced if the intensity is sufficient. A flat top beam can be realized by using only the middle part of the beam (i.e. cutting off the outer area). Otherwise, a beam shaping module would be needed, which would complicate the optical setup. The beam quality is also an important point. Neither a tungsten-halogen, nor a laser-arc source can be expected to deliver nearly monomode beam quality, which would lead to degradation of the image properties. A suitable option for the white light laser would be a “SuperK FIANIUM” by NKT photonics. This light source emits a light spot with a low divergence angle of < 1 mrad in the wavelength range from 410-2400 nm. This type of laser is available with different power levels, delivering up to 5 mW/nm in a FIU-15. The light from the laser can be monochromatized based on holographic transmission gratings in a Laser Line Tunable Filter (LLTF). The monochromator is connected to the measurement system with a monomode fiber, from which the light emerges with a numerical aperture of NA = 0.09 to 0.17, depending on the wavelength. The estimated power from the fiber of a white light laser with a modified LLTF and the intensity distribution on the sample is shown in Figure 2.

Figure 2:

Estimated spectral bandwidth (blue) and performance of the FIU-15 and modified LLTF (left). 2D distribution of the incident light on the substrate (right). The strongest deviation on the sample in X direction: 5% and Y direction: 7%.

2.2

Beam splitter BS

For a measurement at 0°, the reflected beam must be separated from the incident beam. This separation can be done with the help of a beam splitter cube. In the selected wavelength range, it should transmit the measuring beam with 50% and deflect it by 90° with 50%. In addition, the ratio should also be the same for p- and s-polarization. If the cube deviates from this ideal ratio, the efficiency of the beam splitter decreases, because less light is coupled into the sensor. To avoid multiple reflections between the cube and the other components, the cube is tilted by 2°. The acceptance angle of the beam splitter should be designed for this setting. The adjustment can be controlled with the help of a turntable. To avoid multiple reflections in the cube itself, the four optical sides must be anti-reflective (R_avg < 0.6%, R_abs > 1%). The beam splitter cube is available with a clear aperture of 20 mm. The wavefront error of the cube has to be limited since it contributes to the overall error of the setup. A beam splitter with interferometer quality is preferable here.

2.3

Polarizer P

Since the wavefront error is also polarization dependent, the polarization angle of the beam should be set for an accurate measurement. A Glan-Thompson polarizer is suitable for this. Dichroic polarizers, with wavelength-dependent resonances, could introduce large wavefront errors into the system. They are unsuitable. Glan-Taylor polarizers create an internal ghost due to an air gap and are therefore also unsuitable. Glan-Thompson polarizers are available in interferometer quality (wavefront distortion of λ/10) and a clear aperture of 12.6 mm. Since the free aperture of the component limits the maximum size of the beam, all other imaging components such as mirrors or lenses must be matched. In order to avoid multiple reflections to other components here as well, the polarizer is tilted by -2° using a rotating platform. The acceptance angle of the polarizer should also be designed for this setting. The position of the polarizer can be adjusted via a motorized turntable. During a calibration procedure, the optimal setting for p- and s-polarization must be found before the wavefront measurement. An intensity measurement at the Brewster angle of a quartz glass is suitable for this.

2.4

Sample holder S

For exact mounting, the substrate should be positioned on polyetheretherketone (PEEK) rollers and adjusted using positioning platforms. To protect the substrate, the holder is equipped with PEEK edge protectors. This ensures that the substrate does not come into contact with metal. The substrate can be stored standing on rollers. The expected surface deformation of the substrate due to gravity was estimated to be at maximum 0.25 nm with help of a COMSOL simulation. In addition to the roll diameter and substrate thickness, the material properties are important parameters for the simulation. The sample holder (left) and the deformation in the Z direction (right) are shown in Figure 3 below.

Figure 3:

Specimen holder with positioning platform (left), simulated surface deformation in the Z direction (right).

3.1

Referencing

Since wavefront measurements are relative measurements, the setup must be calibrated using a reference substrate. The reference substrate is a flat surface that is precisely measured. It is not coated with a dielectric filter, so the wavefront error in reflection is only dependent on the surface of the substrate and not on the wavelength. In the calibration, the reference substrate is measured instead of the sample substrate. If this calibration is done manually, system changes such as vibrations or air turbulence can be generated, which is why a motorized setting is preferable here. This makes it easy and quick to change between the sample and the reference. The default settings for optimal positioning can also be saved by the system. The sample turntable with reference and sample is shown below in Figure 4.

Figure 4:

Turntable with reference and sample for automated switching between both substrates.

The measurement accuracy of the substrate wavefront error is limited by the calibration accuracy of the measurement system. In order to increase the accuracy, the measurement of the reference substrate is of particularly high importance. The flatness of the sample could be determined with an interferometric calibration measurement. The measurement is based on a Fizeau interferometer that can measure surfaces with a diameter of up to 300 mm. The extended measurement accuracy (k = 2 corresponds to ±2 sigma) is 11 nm peak to valley (PtV) [10]. This means that 95.45% of the measurement data points are within 11 nm. The standard deviation of the calibrated surface deviation is therefore σ = 2.75 nm PtV. The contribution to the wavefront error would be 5.5 nm (1σ) (PtV), since the reflection doubles the contribution. This corresponds to 1.1 nm RMS, assuming that RMS error = PtV/5. In order to avoid errors when holding the sample, the flat is measured in the holder used during calibration.

3.2

Shack-Hartmann sensor

A Shack-Hartmann sensor is recommended to determine the deformation of the wavefront. Within this sensor, a microlens array is positioned in front of an image sensor such as a CCD or CMOS array. If the incoming wave hits the microlens array at an angle due to the wavefront error, the spots behind the individual lenses are deflected. The spatial deviation of the spots between the measurement of the reference substrate and the sample can then be used to reconstruct the wavefront. With an evaluation software, the wavefront error can be approximated with Zernike polynomials. In order to increase the sensor accuracy in the measuring range, the focus length of the microlenses, number of microlenses and lens pitch should be optimized. The required minimum number of lenses (N) depends on the mode (M) of the Zernike polynomials and can be determined with the equation 2N ≥ M [11]. Since high frequency errors of the sample should also be measured, an approximation with up to 55 Zernike polynomials is important. This degree of polynomials corresponds to M = 9, so at least 18 lenses should be illuminated. Using more microlenses can reduce the scanning error and thus the reconstruction error until the numerical errors are in the same order of magnitude as the scanning error [11]. Therefore, a higher number of microlenses is preferable. When projected onto the sensor, the image of the substrate is downscaled by a factor of 11. In a sensor with a lens pitch of 150 μm, 71 lenses are illuminated in one direction at an angle of incidence of 0°. The focal length of the microlens array determines how sensitive the sensor reacts to the wavefront error. Arrays with smaller focal lengths can measure higher slopes in the wavefront errors. The longer the focal length, the finer the effect of wavefront errors and the more stable the measurement results can be determined [12]. However, the focal length cannot be designed too long, otherwise wavelength-dependent diffraction effects from the microlens array may occur. For example, an orthogonal array with a lens pitch of d = 150 μm and a focal length of f = 13 mm can generate stable measurements in the UV range, but cannot measure accurately in the NIR range due to disruptive diffraction effects. The spot image on a Shack-Hartmann sensor for the wavelength λ = 1064 nm is shown in Figure 5 below. In addition to the diffraction images in the spots, the image with a focal length of 13 mm is also overlaid with other diffraction images.

Figure 5:

Spot image measured on Optocraft’s Shack-Hartmann sensor UHR3 at a wavelength of 1064 nm. The array’s lens pitch is 0.15 mm and the focal length is f = 13 mm (left) and f = 9.5 mm (right).

Based on these results, the reproducibility was subsequently determined for a self-assembled Shack-Hartmann sensor together with Optocraft. The lens array was selected with a focal length of f = 9.5 mm and a pixel pitch of 150 μm. Not only the lens array is important for the reproducibility and accuracy of the wavefront sensor, but also the image sensor properties such as pixel size, signal noise ratio (SNR) and bit depth are important parameters. The CMOS sensor IMX367 from Sony with a pixel size of 3.45 μm × 3.45 μm, 12 bit depth and an SNR of 1:4478 was used as the image sensor. The repeatability, the difference between two measurements, was determined three times at three different wavelengths. 66 lenses were used for the measurement. The maximum deviation in this measurement was 0.97 nm RMS. The data determined are shown in the Table 2 below. According to the Optocraft, this image sensor with a microlens pitch of 0.13 and a focal length of 3.3 mm has a repeatability of 3 nm in the same wavelength range [13].

Table 2:

Determined repeatability of the sensor configuration: focal length 9.5 mm; lens pitch 0.15 mm; pixel size 3.45 μm x 3.45 μm for the Wavelength 532 nm, 635 nm and 1064 nm.

3.3

Ghost images

Ghost images can lead to possible errors in the wavefront measurement. The main reasons of ghost images, like the polarizer and the beam splitter, can be eliminated by tilting the components. Nevertheless, there are other contributions that cannot be prevented so easily. Therefore, a ghost image analysis was performed for the measurement system by using the TracePro software. Radiation components with a minimum of 10^-7 of the input intensity were tracked in the simulation. Beams with a lower intensity are not tracked and are no longer included in the simulation. At an AOI of 0°, the Shack-Hartmann sensor has a ghost image with 1.43% of the intensity of the main image. The main part is caused by multiple reflections at the beam splitter. This result can only be achieved by anti-reflective coatings on all optical surfaces of the beam splitter (R_avg < 0.6% and R_abs < 1%). A ghost of 0.03% was determined for the measurements with an AOI of 4° - 20°. This low ghost value can only be achieved because no beam splitter is needed at a higher angle of incidence.

3.4

Measurement accuracy

To determine the influence of the ghost and the accuracy of the sensor, the Shack-Hartmann spot image of a deformed wavefront was simulated with the software ZEMAX. Before evaluating the spot image with the Shack-Hartmann evaluations software SHS Works from Optocraft, it can be optionally superimposed with an artificial ghost image of 1.43% intensity. The determined wavefronts were compared with each other and with the wavefront entering the ZEMAX simulation. The array had a focal length of 9.5 mm and a lens pitch of 150μm. The measurement system was described with the Zernike polynomials 1-36 and a wavefront error of 531 nm PtV and 98.5 nm RMS in ZEMAX. The sample was described with the Zernike polynomials 1-55 and a wavefront error of 317.85 nm PtV and 76.62 nm RMS. A ghost image was superimposed on both the reference image and the sample image. The determined wavefront error is strongly dependent on the parameters in the evaluation software (threshold, pixel for a peak, offset etc.). In a direct comparison, the determined wavefront error with a ghost image is 0.11 nm PtV higher than the evaluation without a ghost image. The RMS wavefront error between the spot image with ghost and without ghost is the same within the framework of the simulation accuracy. The wavefront error used for the simulation is 0.94 nm RMS higher than the wavefront error evaluated with a ghost image. Figure 6 compares the wavefront error before simulating the sensor (left) and after simulating the sensor and reconstructing it using the SHS Works software.

Figure 6:

Workflow to determine the accuracy of the sensor and the influence of a ghost image. A spot image is simulated in ZEMAX with an incoming wavefront error. The SHS Works software is used to reconstruct the wavefront, including the ghost, from the simulated spot image.

The minimum achievable measurement uncertainty can be estimated by considering the results listed above. The measurement reliability of the calibration with the reference substrate (σ_cal = 1.1 nm RMS), the reproducibility of the sensor (σ_rep = 0.91 nm RMS) and the measurement accuracy of the ghost analysis (σ_acc = 0.94 nm RMS) must be considered. According to equation (1) these values can be combined to a minimum measurement uncertainty of 1.74 nm RMS.

3.5

System wavefront error

For more information about the wavefront distortion, the point spread function of the substrate should be measured. In order to keep the influence of the device on the wavefront measurement and point spread function measurements as low as possible, a small wavefront error in the measurement system is preferable. The expected wavefront error was estimated using a Monte Carlo simulation in ZEMAX. The optical components (lenses, mirrors, beam splitters and polarizers) are subject to positioning inaccuracies and shape deviations. The surface shape deviations of the mirrors were generated in ZEMAX with the operand TEZI (Z5-Z36). The Zernike coefficients are chosen from a uniform distribution and then scaled to produce the desired surface form error of 12 nm RMSi. Surface defects (e.g. scratches, dents, etc.) cannot be simulated. Mirrors with such small surface deviations can be made with an electropolished NiP layer. A mirror with a shape deviation of 20 nm RMSi and a diameter of 320 mm was already manufactured in 2014 [14]. Due to the smaller diameter and the iterative manufacturing process, such surface variations are feasible for companies like Spaceoptix. The polarizer and beam splitter can be made with a wavefront error of λ/10. Since the surfaces are flat, only a long-period error (astigmatism and spherical aberration) without power error was assumed. As position uncertainty it was assumed that the light source and the small mirrors can be adjusted in the XY direction with ±3.5 μm and in the Z-direction with ±4.4 μm. This uncertainty corresponds to the path with a 10° turn of the adjustment screw with a pitch of 254.0 μm/rev for the X-Y-direction and 318 μm/rev for the Z-direction. Due to their weight, the size of mirrors or lenses in the structure can only be adjusted using stages with micrometer screws. Therefore, the uncertainty in the X-Y-Z-direction was estimated to ±5 μm.

For the estimation of the system’s total wavefront error, 200 different cases of settings and surface deviations were examined. The maximum of the distribution at 4°-20° wavefront measurement is at 43.5 nm RMS. There is no significant difference in the RMS wavefront error of the system when the sample is measured at an angle of incidence of 4 or 20°. The wavefront error of the system at 0° is slightly higher with 66.5nm RMS. The reason for this is that the same optics are used in the returning beam as in the incoming beam and errors in the adjustment or in the optics have a greater impact. The maximum of the distribution of the system wavefront error for the point spread function measurement is 45.3 nm. This value is higher compared to the other measurement configurations due to an additional mirror.

Figure 7:

Distribution of the wavefront error in the system for the angle of incidence 0° AOI (left), for wavefront measurements with 4-20° AOI (middle) and for measurement from the point spread function with 4-20° (right).