Noise Tolerance of Improved Max-min Scanning Method for Phase Determination

This paper presents and demonstrates the enhancement of noise tolerance exhibited by the improved Max-Min scanning method (IMMS) for phase determination. Numerical simulations and various tests indicate that the IMMS has a good tolerance to certain ranges of noise. One of the IMMS applications, an online method to calibrate the phase shifter, is presented as well. This improved algorithm provides an easy and convenient way to inspect the linearity and the non-uniformity of the phase shifter. It is suitable for use in assessing the reliability of the phase shifting setup in real time. INTRODUCTION The phase shifting technique is a key step in optical measurement. An improved Max-Min scanning method has been described by Ding and Cloud [1, 2]. The principle of it is briefly reviewed in the next section. There is always a serious concern about the environmental tolerance of all kinds of phase determination techniques, because the noise tolerance establishes the limitations on the range of application of the phase shifting techniques. The majority of current techniques require a vibration-isolated table. This paper shows that the application of low-pass filtering and curve fitting techniques to the recorded signals in the time domain improves the noise tolerance of the developed IMMS method. Numerical simulations and tests are presented. One useful application of the IMMS approach is presented in this paper also: calibration of the phase shifter. Generally, a phase shifter, which is usually a mirror mounted on a piezoelectric transducer (PZT), is used to vary one beam path length artificially so as to vary the phase difference between the interfering beams by some supposedly known amount, and then some intensity image signals are captured to calculate the expected phase information [2,3,4,5,6,7]. Although some of these techniques were claimed to be insensitive to phase shifting errors, an efficient real-time calibration of the phase shifter is still desired to understand the effectiveness of the phase shifter and to make phase shifting techniques more accurate. The working status of the phase shifter, such as the demanded driving voltage, non-linearity, stability of the PZT, and the tilt of the mirror, will more or less affect the accuracy of the measurement results. In the past decades, several calibration methods have been developed. They have been categorized into two classes: fringe tracking and the Carré method as described by Hedser Van Brug [8,9]. The fringe locking method is mainly suited with an accurate 2π phase step. The Carré method uses several phase-stepped images to calculate the phase shifting angle by assuming that the phase shifter is linear and uniform, which is likely not true. Neither of these two methods is able to provide the linearity, the tilt, and the non-uniformity of the phase shifter. In this paper, a new real-time calibration method is proposed to calibrate the phase shifting apparatus, as well as to inspect the non-linearity, tilt and non-uniformity of the phase shifter’s movement. IMMS METHOD The principle of the IMMS method is briefly given as follows [1]. The intensity equation of an interferogram is written as ) ( 2 2 1 2 1 φ Cos I I I I I + + = (1) Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 04 JUN 2004 2. REPORT TYPE Journal Article 3. DATES COVERED 04-03-2004 to 08-04-2004 4. TITLE AND SUBTITLE Noise Tolerance of Improved Max-min Scanning Method for Phase Determination 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) Xu Ding; Gary Cloud; Basavaraju Raju 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Mechanical Engineering Dept.,Michigan State University,428 S.Shaw Lane, Rm. 2555,East Lansing,,Mi,48824 8. PERFORMING ORGANIZATION REPORT NUMBER ; #14180 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) U.S. Army TARDEC, 6501 East Eleven Mile Rd, Warren, Mi, 48397-5000 10. SPONSOR/MONITOR’S ACRONYM(S) TARDEC 11. SPONSOR/MONITOR’S REPORT NUMBER(S) #14180 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT This paper presents and demonstrates the enhancement of noise tolerance exhibited by the improved Max-Min scanning method (IMMS) for phase determination. Numerical simulations and various tests indicate that the IMMS has a good tolerance to certain ranges of noise. One of the IMMS applications, an online method to calibrate the phase shifter, is presented as well. This improved algorithm provides an easy and convenient way to inspect the linearity and the non-uniformity of the phase shifter. It is suitable for use in assessing the reliability of the phase shifting setup in real time. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Public Release 18. NUMBER OF PAGES 8 19a. NAME OF RESPONSIBLE PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 where I is the intensity at one pixel, I1 and I2 are the intensities of the two interfering beams respectively, and φ is the phase difference between these two interfering beams at that pixel [3]. From equation (1), the phase angle can be derived as: