1. LabVIEW Program Development for Angle- Multiplexed Spatial-Spectral Interferometry (SSI) Bilan Yang Rice University Dr. Igor Jovanovic Toshiba-Westinghouse Fellows Program The Pennsylvania State University Department of Mechanical and Nuclear Engineering July 31, 2014 1

2. An angle-multiplexed spatial-spectral interferometric measurement can be can be set up with two reference beams and a signal beam. A. Rakhman, M.-W. Lin, I. Jovanovic, Opt. Express 21, 26896 (2013) 2 Component 1 Component 2

3. Filter 1D FFT from x to k A. Rakhman, M.-W. Lin, I. Jovanovic, Opt. Express 21, 26896 (2013) The interferogram is processed according to the reconstruction algorithm of angle-multiplexed SSI. IFFT to x usingusing usingusing Using Divide out 3

4. Polarization state of the signal pulse is represented by amplitudes and various angles. A1, A2: Filtered FFT interferogram amplitudes (laboratory-frame temporal amplitude components) 2 : Orientation Angle 2 : Ellipticity Angle : Spectral phase difference : Auxiliary angle Physikalisches Institut, Appl. Phys. B 74 [Suppl.], S133–S144 (2002) 1 1 2 2 3 3 4 4 4

5. A LabVIEW program achieves real time analysis of SSI according to the retrieval algorithm of spectral phase and polarization state. Control CCD to take Interferogram FFT and IFFT processing Spectral field amplitudes of the references Spectral phase of the signal Spectral field of the signal Orientation Angle Auxiliary Angle Ellipticity Angle 5 Control instrument Control instrument Process with retrieval algorithm Process with retrieval algorithm Retrieve the amplitudes and phase of field components Retrieve the amplitudes and phase of field components Determine the laser pulse polarization state Determine the laser pulse polarization state

6. LabVIEW includes a complete user interface (front panel), allowing for real time analysis during data collection. 6 Control instrument Control instrument

7. LabVIEW processes the Interferogram and retrieve the data efficiently and precisely. 2D interference pattern captured by CCD Fourier Transfer Filtering out sidebands + Inverse-Fourier Transfer 7 Process With Retrieval algorithm Process With Retrieval algorithm

8. LabVIEW processes reference pulses and calculates the spectral field and phase of signal according to the retrieval algorithm. Product of interfering fields Spectral fields of the reference pulses 2D data of reference pulses Spectral field of the signal Retrieved spectrum of signal Spectral phase of the signal The spectrum measured by spectrometer 8 Retrieve The amplitudes and phase of field components Retrieve The amplitudes and phase of field components

9. The retrieved & measured spectrum of signal Spectral field and phase With proper array input, plots can be made easily with XY-Graph function and graph properties can be edited directly on the plots. 9 Retrieve The amplitudes and phase of field components Retrieve The amplitudes and phase of field components

10. LabVIEW goes through the calculation of the complete polarization state exactly as algorithm indicates. Retrieved Ellipticity Angle Retrieved Orientation Angle Retrieved auxiliary Angle Amplitudes (A1, A2) Spectral phase difference Note: calculations shown in the LabVIEW program above but not in the algorithm are for calibration purpose. 1 1 2 2 3 3 4 4 10 Determine the laser pulse Polarization state Determine the laser pulse Polarization state

11. Spectral phase difference between the two polarization components of the signal pulse Retrieved Auxiliary Angle Retrieved Ellipticity Angle Retrieved Orientation Angle The real time characterization of the complete polarization state can be achieved from the spectral field and phase of the signal beam. 11 Determine the laser pulse Polarization state Determine the laser pulse Polarization state

12. Combining the data acquisition and analysis systems helps achieve real time measurement of spectral phase and polarization state by SSI. Interferogram captured by CCD Interface of LabVIEW supported CCD operation program Characterization images of the interfering patterns captured by CCD (SSI Instrument interface) Characterization images Reference and signal data file paths Calibration constants Questions? 12

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