o Conclusion and future work. 2

Robert Brown

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP. o Conclusion and future work. 2

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP. o Conclusion and future work. 3

Linear frequency modulation (LFM) Chirp LFM Chirp Transmitting and echo signal. Trans. Echo Target Time Heterodyne detection Beat frequency Time Heterodyne detection Beat frequency Time Stretch processing 4

Time length = T of signal Bandwidth = B of signal B Slope = = 2π T Time delay = t 1 = 2R c Overlap time = t 1 T LO Echo Detected Signal df B Beat Frequencies = df = 2π t 1 Overlap T t 1 Time df ct Range of target = R = 1 = c 2π(df) 2 2 5

The Fourier transform of the constant frequency (df ) signal is a sinc function. Image point response (IPR) The R is defined as the 3dB frequency width of the sinc function. To improve R the overlap time of the LO and echo signals must increase. 6

Remembering that and are constants, T directly proportional to B= 2π. is A Dirac delta function is the ideal result. 7

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP. o Conclusion and future work. 8

Obtaining truly linear frequency modulation in the optical domain becomes increasingly difficult the larger the modulation bandwidth. There have been recent experiments to generating large bandwidth continuous chirps at optical wavelengths. [1, 2] 9

CREOL temporally stretched a sub 10 picosecond pulse using a Chirped fiber Bragg Grating.[1] Bandwidth = 746 GHz R = 201 μm Published 2010 Temporally stretched, frequency chirped lidar schematic. PC, Polarization Controller; CFBG, Chirped Fiber Bragg Grating; CIRC, Circulator; FL, Fiber Launcher; VOD, Variable Optical Delay; EDFA, Erbium Doped Fiber Amplifier; RFSA, RF Spectrum Analyzer. (Piracha et al.)[1] 10

Lincoln Laboratory aligned different wavelength in a way that when the signal was LFM chirped each chirp aligned end to end before phase matching each connection. LFM chirp applied. = Phase Matching Time Idea behind Lincoln Laboratory experiment. Time 11

(Lincoln Laboratory cont.) Scalable to Bandwidth = 1.5 THz Demonstrated Bandwidth = 20 GHz Scalable to R = 100 μm Published 2008 [2] Setup for generating a 20 GHz, 1 us chirp. LN: lithium niobate, PD photodetector, LO: local oscillator. (Holman et al.)[2] 12

Each experiment produces very large bandwidth LFM chirps but each also has its own difficulty. The power requirements of the CREOL experiment make it hard to imagine a real world system. The phasing of each chirp in the Lincoln Laboratory experiment is a lot of processing at optical wavelengths. 13

Is the process of generating multiple smaller chirps whose bandwidths can be used to produce an effective bandwidth larger than the modulator bandwidth. Normalized Power Spectral Density 1 One Chirp B = 300MHz Three Chirps B eff = 300MHz 0.8 0.6 0.4 0.2 0 700 800 900 1000 1100 f (MHz) Chimenti et al. [3] 14

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP o Conclusion and future work. 15

MFSP uses the same technique as stretch processing but transmits multiple frequencies (n). Multiple transmitting frequencies generate multiple beat frequencies which later can be processed for optimal R. t 1 LO df 2 T Echo Echo Detected Signal (Contains two freq.) Overlap T t 1 df 1 df 2 df 1 B Time 16

Each df differs by the separation in frequency of the laser lines which produced the echo signal. 17

The post processing procedure begins by Fourier transforming the detected signal. FT df 2 Time df 1 18

Knowing the frequency of the information peaks allow us to window each peak separately. 19

After windowing a frequency shift of DF 1,n is applied to each peak of corresponding n. This shift aligns all peaks at. 2π t 1 20

The peaks are inverse Fourier transformed, aligned temporally, and phased matched. 21

Aligning the beat frequencies for all intents and purposes extends the bandwidth. Upper frequency of echo pre processing = post processing translations t 1 Upper frequency of echo post processing Processed Signal Overlap 2 T t 1 Time 22

As expected the simulated results showed an increase in R of n. Stretch Processing Multi Stretch 23

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP o Conclusion and future work. 24

(1) (2) Laser 1 Laser 2 Splitter Coupler Coupler A O M Polarization Splitter (3) RF coupler Target 25

(1) Laser 1 Splitter LO Laser 2 Coupler Coupler Transmitting The multiple frequencies of the transmitting signal are created by two lasers. The LO s polarization is rotated 90 o before recombining with the transmitting signal in the same fiber. 26

(2) A O M LO/ Transmitting The AOM applies an LFM chirp to all the signals. 27

(2) b A O M LO/ Transmitting In our experiment we propagate two independent signals with orthogonal polarizations down the same fiber simultaneously. 28

(3) LO/ Transmitting Polarization Splitter LO Transmitted RF coupler Heterodyned results Echo Target The LO and transmitting signal separated with an polarization bean splitter. The transmitting signal is transmitted and the LO s polarization is rotated 90 o before being recombination with the echo signal. 29

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP o Conclusion and future work. 30

Information peak at df 1 Parasitic peak at DF 1,2. Information peak at df 2 The fiber was not designed to allow propagation down both the slow and fast axis. 31

After windowing and translating the two peaks the gain in resolution can still be observed. 32

The overall results are clear. R for the SP system =117 m while R for the MFSP (n=2) system =51 m. 33

o Concept of stretch processing. o Current procedures to produce linear frequency modulation (LFM) chirps. o How sparse frequency LFM was used for multifrequency stretch processing (MFSP). o How was a MFSP system was created. o Increase in range resolution ( R) achieved by MFSP o Conclusion and future work. 34

The MFSP technique for producing larger bandwidth optical chirps is a viable approach to the present problem. Even when a large spectral bandwidth LFM chirps can be easily produced in the optical regime. MFSP can shorten the time to generate the LFM chirp by n. 35

Create an experiment to increase n. One such way would be to use an acoustic Bragg Grating loop to produce multiple frequencies. Laser 1 Splitter LO PR Coupler A B G Coupler A O M Investigate the possibility of expanding the propagation of two orthogonally polarized signals through the same fiber. 36

During the phase matching portion of the post processing if the two signals were aligned π/2 out of phase a narrow null was produced instead of a peak. This null has a narrower 3dB than the peak of the same bandwidth. Stretch Processing Multi Stretch Stretch Processing Multi Stretch pi/2 out of phase 37

This effort was supported in part by the U.S. Air Force through contract number FA8650 06 2 1081, and the University of Dayton Ladar and Optical Communications Institute (LOCI). The views expressed in this presentation are those of the author and do not reflect on the official policy of the Air Force, Department of Defense or the U.S. Government.

1. Piracha, M. U., Nguyen, D., Mandridis, D., Yilmaz, T., Ozdur, I., Ozharar, S., and Delfyett, P.J., "Range resolved lidar for long distance ranging with sub millimeter resolution," Opt. Express 18, 7184 7189 (2010) http://www.opticsinfobase.org/abstract.cfm?uri=oe 18 7 7184 2. K. W. Holman, D. G. Kocher, and S. Kaushik, "Optical Waveform Generation for Coherent High Resolution Imaging," in Coherent Optical Technologies and Applications, (Optical Society of America, 2008), paper CMB1. http://www.opticsinfobase.org/abstract.cfm?uri=cota 2008 CMB1 3. Chimenti, R. V. (2009). "Sparse Frequency Linearly Frequrncy Modulation Laser Radar Signal Generation, Detection, and Processing". M.S. Thesis Dayton, Ohio: University of Dayton.

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