Data Acquisition and Reduction Algorithm for Shearing Interferometer Based Long Trace Profilometer

Transcription

1 Data Acquisition and Reduction Algorithm for Shearing Interferometer Based Long Trace Profilometer M. Mohamed Ismail and A.K. Saxena Indian Institute of Astrophysics, Koramangala, Bangalore , India ABSTRACT The Long Trace Profilometer (LTP) is a non-contact optical profiling instrument, designed to measure the absolute surface figure to nanometer accuracy of long strip flat, spherical and aspherical X-ray optics of up to 1200mm in length of distance. A key feature of the LTP is the wide range of surface shapes that it can measure. The ease of alignment and great flexibility are a result of the unique LTP optical system. The direct slope measuring capability of the LTP has proven to be very valuable in the measurement of synchrotron beam line optics and other x-ray mirrors[2]. A new polarization Shearing Interferometer based Long Trace Profilometer has been developed and built at Indian Institute of Astrophysics, Bangalore. This paper gives details of the data reduction software for profile calculation at sub pixel level accuracy. Keywords: Data Acquisition, LTP, Babinet Compensator, CCD, Shearing Interferometer. I. INTRODUCTION LTP belongs to the class of Slope-measuring interferometer rather than Height-measuring interferometer. It measures the phase difference between two collinear probe beams as they move across the surface[1]. The LTP system is comprised of an optical head mounted on to an air bearing carriage that traverses a 1200 mm long. The Optical Head consists of a Lateral Shearing Interferometer, which moves linearly sitting on the translational stage in a programmed manner for the local slope measurement, which in turns gives the final profile of the Surface Under Test (SUT). The present LTP is capable of measurement of about 1200mm. Based on the optical configuration parameters an accuracy of 0.1 sec of arc or 1.0 nm in terms of surface height for 1mm segment length can be achieved. The LTP mainly consists of three major components: Optical head, Translation stage, Instrument control and Data acquisition system. II. DESCRIPTION OF THE OPTICAL SETUP A novel beam splitting arrangement produces two sheared beams using Babinet compensator, polarizer s and analyzer. A diode laser source through a polarization preserving fiber optic delivery system has been used as a coherent source for the beams. Which is further divided in to two sets of beams. One set of beam is scanned over the surface under test, while the other is used as a reference. A closed loop ANOLINE LEM-S4 AC Synchronous Brushless Linear servo Motor system with a high-resolution linear encoder provides accurate position information as the carriage is moved along the air-bearing slide. A stable zero optical path difference beam splitter is used to generate the test and reference probe beams, which are imaged by the optical system on to a CCD camera. The interference pattern produced on the detector is a direct measure of the local slope of the surface under test, from which the profile can be derived by integration [5]. The RMS slope error in each measurement point is typically less than arc seconds or nm in terms of surface error. The schematic of an LTP system is given in Fig.1 and Fig 2 shows the LTP Instrument. Fig.1 Schematic of LTP using Polarizing Shearing Interferometer ISSN: Page220

2 between the rays is thus different at different distances from the optical axis of the Babinet Compensator. The angular splitting is given by = 2(n e -n o ) tan 2.1 Optical Head Fig.2 Long Trace Profilometer Where is the wedge angle. For most practical purposes the angle of incidence is close to 90. For =5 the angular splitting is 6 minutes of arc for a Babinet Compensator made of quartz. The path difference between the Ordinary and Extraordinary rays emerging at a distance x from the axis Y-Y (where the actual thickness of the two prisms are equal h1=h2=h) of the Babinet Compensator is shown in Figure b, given by The Optical Head consists of a Lateral Shearing Interferometer, which moves linearly sitting on the translational stage in a programmed manner. In The Optical Head consists of the four main components: Laser Source, Shearing Interferometer, Area CCD detector, Auxiliary Optics. The details of each of the component involved are explained in the following sections Laser Source = 2(n e -n o ) tan x = x The path difference is zero along the axis, where the thicknesses of the two component wedges are equal and increases linearly with x.when such a prism is placed between two suitably oriented polarisers, in the path of a collimated beam one observes a system of straight line fringes to the edges of the component wedge and localized in the interior of the prism. The fringe spacing is equal to The light source with a operating wavelength of nm is used in the Diode Laser source with fiber coupling. This has an advantage because it is monochromatic source of light with a good degree of coherence and easy mountability. The Laser Diode System is fitted with a stabilized laser diode power supply and no special ESD (electrostatic device) precautions are required. The recommended maximum operating ambient temperature for the device is 30C. It has the facility to read the internal temperature using a LM35 sensor Shearing Interferometer A Babinet Compensator (BC) has been conveniently used for shearing/splitting the beam into two. The Babinet Compensator is used for lateral shearing of the wavefront. It consists of two similar wedges cemented together is such a way that the combination forms a plane parallel plate. The optic axis in the two component edges are parallel to the external faces and are mutually perpendicular. This prism splits an incident ray into two rays called ordinary ray and extraordinary ray traveling in different directions as shown in Figure a. The lateral displacement X o = /(2(n e -n o ) tan ) with =9, =0.639 and (ne-no) = (quartz) and focal length of the collimating lense f=500. Beam separation S = f = tan S =1.4 mm Interferogram in the detector plane can be represented by Ordinary Extra Ordinary Fig.3 Babinet Compensator Y x Y ISSN: Page221

3 (W/x) S = n Where W/x is the Slope at a given point n is the Order of the fringe is the Wavelength of the laser beam Calculation of slope error measurement accuracy: Slope at any point of the mirror can be represented by the equation: (W/x) S = n (W/x) S = n Therefore the shift in the fringe n governed by the following equation: n = [(W/x) S] / or slope Error accuracy at any point can be determined by (W/x) = (n / S) for = mm S = 1.4 mm n (1 / 300) This n is based on fringe width and pixel size + subpixel detection of fringe position. (W/x) = (1/300) (1/1.4) = radia = radia sec of arc Hence, Accuracy of measurement of Slope Error = sec of arc In other words minimum detectable slope error amounts to sec of arc Area CCD detector: In order to acquire the interference pattern a CCD Camera is used as the Detector. For our purpose we have used DALSA CA-D7 1024T Camera. It is designed for the most demanding challenges. It offers superior performance, progressive scan, 40 frames per second, outstanding sensitivity and extremely low dark current make the CA-D7 the choice of OEMs and professional around the world. The CA-D7 1024T model camera offers resolution with switch selectable single or dual 12-bit output. Data for 12-bit model is provided at 10MHz. This results in frame rates upto 8 frames/sec. Since LTP requires more resolution, the 12-bit resolution is used and it produces 8 frames/second. Features: resolution, 12 bit dynamic range. 100% fill factor. Frame transfer architecture and pixel reset/exposure control no shutter required. One or two outputs. 25 MHz (8-bit) or 10MHz (12-bit) per output data range. Vertical and horizontal binning options. Snapshot operation Auxiliary Optics Auxiliary optics includes a) Reflecting Mirrors, b) Beam Splitter, c) Focusing Optics, d) Dove Prism a. Reflecting Mirrors Reflectors are thin aluminized glass mirrors kept at 45 so that the light is reflected at an angle of 90. The reflectors are used so that the arrangement is compact. b. Beam Splitter Beam splitter is used to split the incoming beam into two perpendicular directions. One beam is reflected and the other beam is transmitted. The entire surface are better than /10. c. Focusing Optics There are two focusing optics (L1 and L2) introduced in the system. Lens L1 is used to collimate splitted beams from the Babinet compensator and collimate it to produce two sheared beams parallel to each other. Lens L2 is an imaging lens, which helps in focusing the object on to the detector, which is a CCD camera. d. Dove Prism A dove prism is a type of reflective prism which is used to invert an image. Dove prisms ISSN: Page222

4 are shaped from a truncated right-angle prism. It has been used for matching the direction of the shift for both the SUT mirror and Reference mirror. III. Translation Stage Translational stage is the next most important component of the Long Trace Profilometer. The optical head of the LTP requires smooth movement, which is provided by the translation stage with reduced pitch error and yaw error. The Translational stage has been developed by Anorad, and has the following main features. Features: Travel length = 1200 mm (48 inches) Minimum detectable slope error 0.20 arc sec or lower. Range -15 min. Measurement in step of 1mm and above programmable. Overall Positional accuracy = 5m Resolution = 1.0m Slide speed (Alignment mode) = mm/sec Roll error = <3 arc sec Pitch = <3 arc sec Yaw = <3 arc sec Drive control and positioning, data acquisition and reduction through computer control Max. Weight = 800 Kg The main parts of the translation stage are 1. Mechanical slide 2. Motion drive and control 3.1 Mechanical slide The system is based upon a massive granite beam for high precision, stability and vibration damping. All critical surfaces of the granite are lapped for precise geometry. Threaded stainless steel inserts are cemented in the granite for the mounting of the positioning components. The system comprises of a Push and Carrier slide. To prevent heating up of the Carrireslide caused by the motor on the Push slide the two slides are isolated through a pushing rod. The encoder can be mounted on the Carrier or Push slide. See Figure 3.1 for details. Fig.4 Translational Stage 3.2 Motion drive and control CCD Camera The position control of the translation stage is done using a µ-serv-1, which is a powerful and cost effective combination of an advanced programmable controller, with integral digital amplifiers and power supplies, were designed to suit the needs of Anorad's high performance Anoline brushless linear servo motors. The universal drives are software configurable for the following motor types: DC brushless/ac servo, AC induction, DC brush, and stepper. The drive is suitable for motors rated up to 600W. µ-serv- M is 24Vdc to 60Vdc, 7.5A continuous, and 15A peak. The µ-serv-1 supports encoder (+ Hall) or resolver (12 bit resolution) as primary feedback. In addition to dedicated safety inputs, it has eight inputs, eight outputs, one analog input, and one analog output.the SB1381 control module is the combination of an advanced programmable controller Reference and a universal Mirror digital drive. The universal drive is software configurable for the following motor types: AC Servo, DC brush and AC Induction motors. It features automatic sinusoidal commutation setup for AC Servo and AC Induction motors. Two power levels are available: 7.5A (15A peak) 18-40VAC (24-60VDC) and 5A (10A peak) 40-85VAC (60-120VDC). The translation stage was fully tested for its performance using the LTP optical setup and reference beam for calibration. The graph below shows the measurement readings for a distance of 1150mm of the reference beam. 3.3 Computer Control of the translation stage: The position control of the Translation stage is automated using the Lab VIEW software. Figure 1a shows the computer system set up for motion control and data acquisition and analysis. ISSN: Page223

5 carrying out these functions, there are two modes of movements, namely: Incremental Jog and Continuous Jog. Fig.6 shows the front panel. Refer the operation manual for more details on the operation of the front panel. Fig.5 Computer Control of Translational Stage IV. ALGORITHM DESCRIPTION The software development has two major divisions,1) Motion control software 2) Data Acquisition and Processing software. The Motion control software module deals with the motion control of the optical head while taking the measurement. Data Acquisition and processing software module includes Image Grabbing, Image compression, Fringe Shift and Slope measurement along with the final result calculations. 4.1 Motion control software The position control of the translation stage is done using a µ-serv-1, which is a powerful and cost effective combination of an advanced programmable controller, with integral digital amplifiers and power supplies, were designed to suit the needs of Anorad's high performance Anoline brushless linear servo motors. The universal drives are software configurable for the following motor types: DC brushless/ac servo, AC induction, DC brush, and stepper. The dhggrive is suitable for motors rated up to 600W. µ-serv-m is 24Vdc to 60Vdc, 7.5A continuous, and 15A peak. The µ-serv-1 supports encoder (+ Hall) or resolver (12 bit resolution) as primary feedback. In addition to dedicated safety inputs, it has eight inputs, eight outputs, one analog input, and one analog output. The installation and interfacing of this card is explained in the Hardware manual Setup Mode This mode is used for setting up of the various parameters of the instrument for the measurement. The major functions of this mode are: Referencing the axis, Fixing the start and the end positions of measurement and Fixing the number of steps for the measurement. For Fig.6) Setup Mode This module includes 3 major sub divisions namely: a) Image Grab, b) Sub pixel Determination of Fringe Maxima (SDFM) and c) Detrending Shift in Pixel Fig.7) Fringe pattern of the Reference Mirror and Test Mirror on CCD detector Reference 1150mm Disnance in mm Fig.8) Reference beam measurement ISSN: Page224

6 The translation stage was fully tested for its performance using the LTP optical setup and reference beam for calibration. The graph above shows the measurement readings for a distance of 1150mm of the reference beam. This depicts the repeatability of the present LTP II. In the following, a flowchart explained for data acquisition and reduction procedure. A Storing Data on the spread sheet file for the maximum or minimum of the fringe peak Start Image Grabbing Shift calculation (Reference corrected) SUT - Reference Image window sizing for the SUT and the reference. Convert the respective image window into 16bits 2D array of fringe data Compression of the Image Fringe data compression from 2D to 1D array of 1 x 1056 data points Perform first order Polyfit Forward FFT on the Data Peak Selection Slope Calculation Shift = Shift/2; n = Shift/Fringe width; Slope = ( n/shear) * lambda *k; Shear = 1.4; lambda = ; k =3.1; Slope = Slope * dx; dx = 1(default) Inverse FFT on the Data Find the maximum index of the filtered data = A Selection of 3 points on either side of the maximum index => Sub-array of the intensity values at the chosen 7 points of data Integrate and Polyfit (1 st /2 nd order) Generation of 1D array of 60 points by dividing each interval by 10 points Save data and plot. Find the RMS value in microns Polyfit in 3 rd order and find the maxima index of the result = B (A-3) + (B/10) = Final maximum peak value Stop Fig.9) Flow chart for Data Acquisition and Reduction Software A ISSN: Page225

7 IV. CONCLUSION The problem of identifying and analyzing a source of error in slope measurement using an LTP has been discussed. It is seen from the above data and graphs that the LTP is capable of giving very accurate measurement of profiles of complicated optical surfaces and LTP provides an accurate and suitable means of characterizing the optics mirrors. LTP is a versatile metrology instrument for unconventional optics. References [1] Sostero, G., Cocco, D., and Qian, S., Metrological challenges of synchrotron radiation optics, in [Optical Fabrication and Testing], Geyl, R. and Maxwell, J., eds., Proc. SPIE 3739, (1999). [2] Li, Z., Zhao, Y., Li, D., Xiao, T., and Xia, S., A novel long trace profiler for synchrotron radiation optics, Optics & Laser Technology 37, (2005). [3] Takacs, P. Z., Feng, S. K., Church, E. L., Qian, S., and Liu, W., "Long trace profile measurements on cylindrical Aspheres," Proe. SPIE, vol. 966, (1988) 354. [4] Takacs, P., Church, E., Bresloff, C., and Assoufid, L., Improvements in the accuracy and the repeatability of long trace profiler measurements, Applied Optics 38, (1999). [5] P.Z. Takacs, S.N. Qian, and J. Colbert, "Design of a long trace surface profiler, Proc. SPIE 749 (1987) pp [6] Irick, S. C., McKinney, W. R., Lunt, D. L. J., and Takacs, P. Z., "Using a straightness reference in obtaining more accurate surface profiles from a long trace profiler," Review of Scientific instruments, vol. 63, No.1, , (January, 1992). [7] Irick, S. C., "Advancements in one-dimensional profiling with a long trace profiler", Proc. SPIE, vol. 1720, (1992), 162. [8] Irick, S. C., "Determining surface profile from sequential interference patterns from a long trace profiler," Review of Scientific Instruments, vol. 63, No.1, , (January, 1992). [9] Steve Irick, Long trace profiler survey results, Proc. SPIE 3782, (1999). [10] S. N. Qian, G. Sostero and P. Z. Takacs, Precision calibration and systematic error reduction in the long trace profiler, Opt. Eng. 39(1), (2000). ISSN: Page226