SCIENCE CHINA Physics, Mechanics & Astronomy Article April 2014 Vol.57 No.4: 608 614 doi: 10.1007/s11433-013-5264-5 Optimization of the transmitted wavefront for the infrared adaptive optics system YANG PengQian 1,2,3*, HIPPLER Stefan 2 & ZHU JianQiang 1 1 Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China; 2 Max-Planck-Institute for Astronomy, Königstuhl 17, D-69117 Heidelberg, Germany; 3 Graduate University of Chinese Academy of Sciences, Beijing 100049, China Received February 25, 2013; accepted May 8, 2013; published online December 31, 2013 The adaptive optics system for the second-generation Very Large Telescope-interferometer (VLTI) instrument GRAVITY consists of a novel cryogenic near-infrared wavefront sensor to be installed at each of the four unit telescopes of the Very Large Telescope (VLT). Feeding the GRAVITY wavefront sensor with light in the 1.4 2.4 µm band, while suppressing laser light originating from the GRAVITY metrology system requires custom-built optical componets. In this paper, we present the development of a quantitative near-infraredpoint diffraction interferometric characterization technique, which allows measuring the transmitted wavefront error of the silicon entrance windows of the wavefront sensor cryostat. The technique can be readily applied to quantitative phase measurements in the near-infrared regime. Moreover, by employing a slightly off-axis optical setup, the proposed method can optimize the required spatial resolution and enable real time measurement capabilities. The feasibility of the proposed setup is demonstrated, followed by a theoretical analysis and experimental results. Our experimental results show that the phase error repeatability in the nanometer regime can be achieved. adaptive optics, non-common aberration, point diffraction interferometry PACS number(s): 95.75.Qr, 42.87.-d, 42.30.Ms Citation: Yang P Q, Hippler S, Zhu J Q. Optimization of the transmitted wavefront for the infrared adaptive optics system. Sci China-Phys Mech Astron, 2014, 57: 608614, doi: 10.1007/s11433-013-5264-5 1 Introduction The GRAVITY wavefront sensor (WFS) is part of the second generation Very Large Telescope-interferometer (VLTI) instrument GRAVITY [1]. The GRAVITY WFS provides a complete adaptive optics system, which can be generally used at the VLTI due to its stand-alone character. It adds near-infrared wavefront sensing at the 8.2-m Unit Telescopes for use with VLTI [2 4] and as such complements the available visible wavefront sensing MACAO systems [5]. The goal of GRAVITY is to measure relative positions on the sky, i.e., the separation of 2 objects, at a level of the *Corresponding author (email: yangpengqian@siom.ac.cn) order of 10 micro-arcseconds on the sky. For this purpose, a sophisticated metrology system has been designed [6]. The basic idea of the metrology system is to sample the optical path of the incoming telescope beams as completely as possible, with a precision of about 1 nm (rms differential optical path difference of 2 objects separated by about 1 on sky). In the GRAVITY design this is accomplished through placing a near-infrared laser between the beam combiner and the science detector, and projecting its light backwards through the instrument towards the secondary mirror of the Very Large Telescope (VLT) unit telescope M2. The near-infrared wavefront sensors are located between the delay lines and the telescope main optics, near the Coudé focal station of the telescopes. The principle is shown in Figure 1. As the metrology laser s wavelength is at 1.908 Science China Press and Springer-Verlag Berlin Heidelberg 2013 phys.scichina.com link.springer.com
Yang P Q, et al. Sci China-Phys Mech Astron April (2014) Vol. 57 No. 4 609 Figure 1 Principle of the GRAVITY metrology system shown for two telescopes. A laser beam travels the same path backwards through all the beam combination and the VLTI optical train. Detection of the resulting fringe pattern takes place close to the entrance pupil (M2), above the primary mirror M1, by sampling the pattern at four locations with photodiodes, and after reflected by the secondary mirror (M2), the beam was relayed to the delay line. The near-infrared wavefront sensors are located in between the delay lines and the telescope s main optics, precisely at the Coudé focal station of each VLT unit telescope. µm, the near-infrared wavefront sensors will be sensitive to the very bright laser beacon. Furthermore, the design foresees an injection power into the beam combiner optics of 2 W. The implication of this bright beacon is that anentrance window with an optical density of >OD8 at the metrology wavelength of 1.908 µm has to be implemented to protect the WFS from this artificial signal. In the current paper, we show the results of the transmitted wavefront error (WFE) measurements through the entrance windows of the GRAVITY WFS system [7]. In order to determine the transmitted WFE performance of the entrance windows in the near infrared wavelength range, we used a slightly off-axis point diffraction interferometer (SOPDI) based on the Michelson [8,9] configuration. This configuration allows optimizing the spatial resolution. In combination with a fast near-infrared camera the complete setup enables real-time measurement capabilities. The proposed SOPDI distinguishes itself by the possibility to measure with a single shot and being built with simple off-the-shelf optical components. In sect. 2 we describe in detail the optical component under test. The system layout and the SOPDI principle are presented in sect. 3.1. Following this step, the principle of the windowed Fourier filtering (WFF) algorithm for phase reconstruction is detailed in sect. 3.2. To verify the feasibility of the proposed method, we performed an experiment and made stability tests. This is described in sect. 3.3. We conclude in sect. 4. entrance windows are considered to be one of the key elements for the WFS cryostat of the GRAVITY near-infrared WFS. The importance of the blocking filters to the GRAVITY adaptive optics system is such that all four units of the WFS designs require such coated entrance windows. The blocking filter serves as notch filter for the 1.908 µm metrology laser light, and the suppression should be better than 10 8 to prevent the background radiation from saturating the detector and decreasing the signal to noise ratio of the WFS. The spectral transmission measurements were performed using a spectro-photometer. It is well known that silicon windows do not transmit wavelengths shorter than about 1.3 µm. The detailed spectral transmission within a wavelength range between 1500 nm and 2100 nm is shown in Figure 2. The total budget of the WFE in the optical design of the GRAVITY WFS is critical for providing the necessary 2 Design of the metrology laser blocking filter for the WFS The multi-layer coated blocking filters on top of the silicon Figure 2 (Color online) Spectral transmission of the MENLO laser, the laser band-pass filter, and entrance window with the metrology blocking filter.
610 Yang P Q, et al. Sci China-Phys Mech Astron April (2014) Vol. 57 No. 4 accuracy wavefront measurement to meet the scientific requirement. The challenge is to avoid the wavefront distortion introduced by the entrance window being coupled into the detected wavefront. These distortions cannot be corrected with the deformable mirror, since the distortions appear only in the non-common path (see Figure 3). In addition, the small non-uniformity or imperfections in these multilayer coatings may introduce unacceptable wavefront errors. Moreover, these errors depend on the wavelength in a rather complex manner. The non-common path aberrations would degrade the contrast of final image of WFS. As a result of this design, a high quality of the transmitted wavefront should be maintained to access the promising wavefront detection of the GRAVITY s AO system. 3 Characterization of the entrance window in the near-infrared spectral range Point diffraction interferometry plays an important role in the field of optical science and optical engineering, and has been used extensively in diverse applications such as phase profile quality of wavefront deformations [10 12]. It can provide a noninvasive high resolution phase map of the whole field under test. The basic principle of the point diffraction interferometer is to generate a diffracted wavefront internally, the so called self-referencing. Point diffraction interferometry is much less sensitive to certain types of environmental disturbances such as mechanical vibration, temperature fluctuations, and air turbulence. These unique features are due to the common path geometry and the reliable phase retrieval algorithm. To characterize the wavefront propagation error in transmission, we developed a Michelson architecture based near-infrared point diffraction interferometer, and implemented the local windowed Fourier transform (WFT) algorithm for amplitude and phase extraction. This instrument was applied to study the trans- Figure 3 Sketch of the GRAVITY adaptive optics system. A beamsplitter inside the Star separator marks the point where common optical path and non-common optical paths between the WFS and the beam combiner instrument separate. mitted wavefront quality of the cryostat entrance windows, which were designed for the GRAVITY WFS. With the optical setup shown in Figure 4, the SOPDI to characterize near-infrared transmitted wavefronts, and the help of the WFT filtering algorithm, we analyzed the phase information of the measured single carrier interferograms. 3.1 Optical setup of the IR-point diffraction interferometer The optical configuration of the proposed infrared SOPDI is sketched in Figure 4. Briefly, the fiber coupled near the infrared frequency-stabilized laser with a wavelength of 1523 nm is collimated and used to illuminate the sample in transmission. The neutral density filters are used to control the intensity of the laser beam. After the collimated beam passes through the test specimen, a lens (L2) is located behind the test specimen to convert the beam into converging beam. The converging beam of the laser beam falls onto the infrared non-polarizing cube beam splitter (NPBS) and then splits into a transmission beam and a reflection beam. The two beams from the beam splitter are incident on the gold-coated mirrors and reflected at their Fourier plane, and recombined by the beam splitter. The reflection beam is low-pass filtered by using the pinhole spatial filter positioned in the spatial filter plane, which is the Fourier plane of L2, and transformed as the reference wave. The accuracy of PDI method largely depends on the accuracy of the diffracted spherical wave [10]. To guarantee the quality of the illumination, the pinhole diameter of 25 µm was selected, which is approximately 1.4 times the half of the Airy disc given by d=1.22f 2 /D, where =1523 nm is the wavelength, D (10 mm) is the input diameter of the collimated beam, and f 2 is the focal length of L2 (see Figure 4). Another lens (L3) was placed in the conjugate position of the first lens (L2) to form a 1:1 4f spatial filtering system. The first lens performs the Fourier transform of the input field of the object, the transformed field is then filtered by the pinhole, and then the product is Fourier transformed again by L3. The M1 mirrors normal has a small angle with respect to the optical axial direction, and thus the reflection beam travels in a direction with a small angular offset to the optical axis, and the slightly off-axis fringe pattern is formed. A diaphragm in the Fourier plane of the telescope system is used as the field stop to eliminate ghost images and other unexpected stray light. An infrared camera is located at the back of a 4f imaging system to capture the fringe pattern. Since the sample beam only splits at the end of the optical chain, the proposed setup can be considered a quasi-common-path interferometer, and its stability will be significantly higher compared to conventional interferometers. For simplicity, we denote the object wave after passing through the test specimen as O o (x, y). Considering a tilted angle introduced by mirror M1, the reference wave can be
Yang P Q, et al. Sci China-Phys Mech Astron April (2014) Vol. 57 No. 4 611 In this section, the wavefront reconstruction method of the slightly off-axis interferometry is introduced. In the off-axis configuration, the angle between the object and reference waves introduces a carrier-frequency modulation in the interference pattern. The Fourier transform method is a powerful tool for demodulation of carrier fringes [11,13,14]. However, Fourier transform method is a global transformation with poor spatial localization, which also leads to the degradation of phase frequencies of the interferograms. To overcome this shortcoming, we used the method for reconstructing phase and amplitude from a single carrier frequency interferogram by using a WFT method in our experiment. The intensity distribution of a carrier-frequency fringe pattern recorded on the image plane is described as: f ( xy, ) axy (, ) bxy (, )cos( ( xy, ) ( xy, )). (2) Here, axy (, ) O R ; bxy (, ) 2 O R; and ( xy, ) denotes the phase distribution of the specimen. In order to reconstruct the fringe with the image free of the zero order, the direct current (DC) term can be suppressed by subtracting the average intensity from the interferogram [15], and the interferogram can be derived as: f ( xy, ) cos( ( xy, ) ( xy, )). (3) Figure 4 Diagram of the experimental arrangement used for SOPDI for compact setup with common path configuration at 1523 nm wavelength; L1 L5, achromatic lenses; focal lengths of the lenses f 1 =200 mm, f 2 =f 3 = 100 mm, f 4 =150 mm, f 5 =45 mm; PH, pinhole filter with diameter 25 µm, NPBS. expressed as: R x y FT FT O x y T x y (1) 1 (, ) { [ o(, )] PH}exp[i (, )], where FT[] and FT 1 [] denotes the 2D Fourier transform and the 2D inverse Fourier transform, respectively. The FT 1 { FT[ O( x, y)] T PH } denotes the average or nondiffracted component of the object wave obtained by the pinhole filtering. T PH denotes the transmittance of the pinhole filter; ( xy, ) is the spatial frequency induced by the tip/tilt of the M1 respect to the optical axis. Here, the carrier frequencies can be determined from the fringes of the off-axis interferogram. It should be noticed that the intensity of the reference wave is much lower than the intensity of the signal wave after the pinhole filtering. To ensure the best possible signal-to-noise ratio, maximize the fringe contrast provided by the interferometer. Either a variable neutral density filter or the coating method [12] can be applied, with which adjustable contrast of the fringe pattern can be realized by adjusting the relative intensities of interfering waves. 3.2 WFF for carrier fringe phase retrieval After the DC term suppressed interferogram is obtained, the complex distribution of the object wave in the recording plane can be calculated with the WFF method as follows. The 2-D WFT and inverse WFT (IWFT) are written as: ' * uv,,, (4) Sf ( u, v,, ) f ( x, y) g ( x, y)dxd y, 1 f ( xy, ) Sfuv (,,, ) g ( xy, )dxy d, 4 2 uv,,, (5) where f (x,y) is the original signal; Sf ( u, v,, ) denotes the spectrum of WFT; and guv,,, ( x, y) is the WFT basis, which can be expressed as: guv,,, ( x, y) g( xu, yv) exp( jx jy), (6) where (x, y), (, ) are the translation and frequency coordinates respectively,and g(x, y) denotes the windowing function. When g(x, y) is Gaussian function,the WFT turns to be Garbor transform: The parameters 1 x y gxy (, ) exp. 2x 2 x y y x and (7) y are the extension of g(x, y) in x and y, respectively. The Gaussian window is often chosen for the local frequency spectrum filtering as it provides the smallest Heisenberg box [16], which permits the WFT to provide best frequency information of the limited region around each pixel. By combining eqs. (2) (7), 1 f( x, y) Sf( u, v,, ) 4 1 1 g ( x, y)dddud v, xy,,, where Sf ( u, v,, ), if Sf ( u, v,, ) threshold, Sf ( u, v,, ) 0, i f Sf ( u, v,, ) threshold. (9) (8)
612 Yang P Q, et al. Sci China-Phys Mech Astron April (2014) Vol. 57 No. 4 According to eqs. (8) and (9), only limited spectrum range of the signal (frequencies of the fringe pattern) should be computed by adjusting and, and the background noise was sufficiently suppressed in terms of its amplitude. The window size for the WFT must be optimized to reduce the errors introduced near the boundaries and random background illumination.in this study, window size (4 x 1) (4 y 1) is set to achieve an optimal estimation for phase deformation [17]. Once the 4D coefficients are computed, the filtered fringe pattern and estimated distribution can be obtained as: 1 Im f ( xy, ) ( xy, ) tan. Re f ( xy, ) (10) Phase ambiguities will still exist after the Fourier transformed local frequency spectrum filtering. This is exactly the same phase unwrapping issue that exists in the standard fringe analysis. Next, an unwrapping algorithm is applied to obtain the final wrapped object phase [18,19]. After removal of the 2 ambiguity by a phase unwrapping process, the total phase information can be obtained. By using the above mentioned reconstruction method, the phase distribution of the tested specimen is obtained. Single-shot frame instantaneous interferometry offers an alternative optical test method where environmental noise prohibits conventional phase shifting methods. The advantage of the slightly off-axis interferometry scheme compared with the traditional off-axis interferometry is analyzed in the following. The on-axis interferometry can make full use of the resolving power of the detector [20,21], and thus has the advantage of high spatial details over the off-axis scheme. However, in this case at least three of the time sequential phase-shifting interferograms have to be acquired to reconstruct the original wavefront under the test. While the WFT spectrum analysis method provides pixel sized frequency information of the whole field, the traditional Fourier transform is impossible. In the traditional off-axis scheme, the twin image, DCterm and real image of the interferogram have to be separated. This requires the carrier frequency to be at least three times the maximal spatial frequency (f 0 ) of the object wave to isolate the side band image. As a result, four times the bandwidth of the object wave is required to record the off-axis interferogram [20]. This will decrease the resolving power of the detector array at some level, and also introduce ray trace errors due to the off-axis configuration. However, this is unnecessary for our proposed method as the separation is realized by simply subtracting the average intensity of the fringe pattern. As WFT is a local transform from pixel to pixel, the transform is more tolerant to the quality of the wrapped phase map, and this also makes the filtering more effective in eliminating the low amplitude noise. The slightly off-axis method only requires carrier frequency k f 0 to separate the two conjugated items, resulting in the optimal detector sampling frequency k d 2 f 0, only half of that needed in the traditional off-axis interferometry. Above all, the off-axis scheme has real-time measurement ability and is less sensitive to the localized signal errors. The proposed off-axis scheme enables us to achieve higher spatial resolution as well as real-time measurement capability. 3.3 Experimental results and analysis To demonstrate the feasibility of the proposed system we used an experimental setup as shown in Figure 4. The infrared camera (FLIR SC 2000, FLIR Systems Inc.) has a maximum acquisition rate of 206 frames/s at the full resolution of 320 256 pixels and with a pixel size of 30 μm (H) 30 μm (V). The imaging system has a magnification of 3.3, so that the cosine modulation of the fringe is approximately sampled by 10 pixels per period. In our experiment, an entrance window designed for the adaptive WFS cryostat of GRAVITY was used as specimen. Figure 5(b) shows the complex amplitude of the object wave as retrieved by using WFF method, where the phase is still wrapped. The reconstructed OPD of the specimen is given in Figure 5(c), after the phase has been unwrapped. To remove the background, the phase retrieval procedure requires measuring the background phase of the setup without the test optics. This background phase subtraction allows us to correct the residual errors associated with the experimental setup. The measurement is taken without the presence of the specimen. Using these data, the wrapped background phase can be calculated. A comparison of the centerline profiles obtained with the proposed setup and a prototype step phase shifting interferometer (PSI) from TRIOPTICS GmbH is shown in Figure 6. A BK7 made optical window, which transmits in both the optical and infrared region, was employed to perform the measurements. The resulting height errors of ~3.3 nm rms of the centerline profile confirm the excellent performance achieved by the proposed system compared to the PSI measurement. Figure 7(a) shows the interferogram of the entrance window captured using the near infrared SOPDI. The reconstructed wavefront deformation (see Figure 7(b)) Figure 5 Experimental results based on off-axis Window Fourier Filtering interferometry. (a) Typical slightly off-axis interferogram of a multi-layer coated optical window; (b) wrapped phase distribution extracted as the mean of Windowed Fourier transformed spatial filtering method; (c) reconstructed object wave.
Yang P Q, et al. Sci China-Phys Mech Astron April (2014) Vol. 57 No. 4 613 Figure 8 Stability test for the proposed setup in nanometers associated with the background of the full field view (dashed line) and a single point phase profile (solid line). Figure 6 The center line profiles of the test ofa BK7 optical window measured with SOPDI and a PSI. Figure 7 Measured transmitted WFE of the test entrance window. (a) Single slightly off-axis interferogram captured by the near infrared SOPDI; (b) Zernike fit of the wavefront deviation of a central circular part of the entrance window with a diameter of 15 mm. The Zernike fit is calculated to a maximum of the first 36th terms, and only piston and tip/tilt values have been removed. is represented by a set of the orthogonal functions with suitable coefficients [21,22]. Here the Zernike polynomials were implemented as the set of orthogonal functions. After subtraction of focus and tip-tilt terms, the final WFE is 10.2 nm rms. Since the diameter of footprint of the metrology beam on the entrance window is smaller than 1.5 mm, the WFE performance of the entrance window meets the GRAVTY specification (which is 60 nm rms). To quantify the stability of the instrument against environmental disturbances, and thus identify the repeatability of measurements, we continuously measured sets of 100 frames without the sample, with intervals of 18 s (covering total 30 min). The integration time of infrared camera is about 10 ms for each frame. The optical path difference associated with the full field of background phase map has a standard deviation of 3.22 nm, as shown in Figure 8, which verifies high repeatability of the proposed setup. An arbitrary 4 4 pixel average point, characterized by a standard deviation of 10.8 nm, is also shown in Figure 8, which shows long term stability of the proposed setup. Obviously, the quasi-common-path design significantly minimizes the systematic errors and ensures the high repeatability and stability. It should be noted that the proposed setup can be also used for on-axis parallel phase-shifting point-diffraction interferometry. When the M1 is placed perpendicular to the optical axis, on-axis interferograms can be obtained. Compared with the off-axis scheme, the on-axis configuration can make full use of CCD camera spatial resolving power, and provide more spatial details of the sample. However, it requires the time series phase-shifting interferograms to do the phase retrieval, which may make the system more complex. This configuration could also be used for multi-wavelength without changing the main optical elements. The two primary error sources that limit the accuracy of the PDI are the errors generated by the pinhole spatial filter and the systematic error from the system geometry [7]. Basically, the systematic geometric errors could be simply removed in the background calibration process. Considering the pinhole induced errors vary randomly as a function of reference pinhole position, the test object can be suppressed through averaging. 4 Conclusion In summary, we present the near infrared point-diffraction interferometry as a novel approach to studying transmitted wavefront quality in the near-infrared band, with a promising accuracy. The proposed setup is compact, less vibration sensitive, and sufficient for the dynamic process measurement. The major advantage of the setup is the simplicity, high temporal stability and its potential low cost. The carrier frequency is introduced by slightly tilting one mirror with adjustable tip/tilt. Thus, the phase information can be directly extracted from a single interferogram with a spatial carrier method in real time. The Windowed Fourier spatial analysis technique allows us to obtain higher spatial resolution with respect to the traditional off-axis setup. The high temporal stability enables the investigation of dynamical processes. These advantages are also good for dynamical process measurements and advanced wavefront sensing in many other applications.
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