A Segmented Chirped-Pulse Fourier Transform Millimeter Wave Spectrometer ( GHz) with Real-time Signal Averaging Capability Brent J. Harris, Amanda L. Steber, and Brooks H.Pate Department of Chemistry University of Virginia

Segmented CP-FT: Single Spectrum Acquired in 100  s 100 µs, 35 GHz (260 – 295 GHz) Simple Benchtop Prototype 65 cm sample cell

Advantages for Chirped Pulse mm-wave Spectroscopy A. Steber, B. Harris, J. Neill, B. Pate, J. Mol. Spec 280 (2012) )Rapid spectrum acquisition (35 GHz spectrum acquired in 2  s) 2)Coherent measurement methods for spectrum analysis 3)Transition frequency accuracy 4)Simple spectrum signal processing (no baseline effects) Challenges for Chirped Pulse mm-wave Spectroscopy 1)Real-time signal averaging to achieve high sensitivity 2)Reduction of spurious signals 3)Spectral resolution and Fourier transform signal processing

Instrument Design Principles: The Chirped Pulse 1)The Chirped Pulsed Separates the Pulse Duration from the Pulse Bandwidth High-Resolution Spectroscopy: Line width is much smaller than frequency range Line width: set by the signal dephasing (Doppler, Collisional Relaxation) Optimal Excitation Pulse Duration: ~ 1 / (line width) Transform Limited Pulse Duration: ~ 1 / (frequency range) 2) In the Weak Pulse Limit the Signal is proportional to (Bandwidth) -1/2 Signals for transform limited pulses scale with (Bandwidth) -1 : Spectral energy density reduced by both increased bandwidth and shorter pulse duration.

Instrument Design Principles: Segmenting Segmenting the Measurement Frequency Range Relative Segment Bandwidth: (1/N) Rel.Signal in Segment: (2) ½ Reduction in Averages: ½ Rel. Measurement Time: 2 * ½ = 1 Full Bandwidth CP-FT Rel. Signal in Segment: (N) ½ Reduction in Averages: (1/N) Rel. Measurement Time: N * (1/N) = 1 Things that are segment independent (all things being equal): 1)The time required to reach a target dynamic range (signal-to-noise ratio) 2)The number of points that make up the spectrum For smaller segments, lower digitizer rates can be used (Transform limited pulses: increasing the segment bandwidth increases the measurement time!)

Instrument Design Principles: Segmenting Segmenting the Measurement Frequency Range Things that are segment dependent (all things being equal): 1)The time required for one spectrum scan (N times longer) 2)The total number of data points processed (Reduced by N) Molecules perform some of the averaging Things that are not equal: 1)Digitizer cost and real-time signal averaging performance (favors more segments) Still need bandwidth to use power efficiently and minimizing stitching 2) Proliferation of spurious signals (favors more segments) Exception: Single Segment has best mm-wave practical spur performance

GHz CP-FT Design for Real Time Averaging Number of Spectrum Points: 35 GHz frequency range, ~ 2  s dephasing time Minimum Points: (70 Gs/s) x (2  s) = 140,000 This number of data points can be accommodated in FPGA accumulator 512K points maximum, 8-bit digitizer, 32-bit data size Maximum real-time accumulations: 2 (32-8) = 2 24 = 16M Minimizing the Spurious Signals:Strongly Dependent on AWG purity for LO generation LO Impurity Spurs:LO-to-IF Conversion (self mixing): Easily subtracted Spectrum Images: Improved AWG performance on N*30 MHz This fixes the segment bandwidth to 30MHz x 24 = 720 MHz: 50 segments, 100  s scan time Digitizer/Receiver Spurs: Second Order IM: work in 2 nd Nyquist zone (720 – 1440 MHz) Third Order (Two-tone IM) Signal/Clock Mixing in Digitizer

Segmented Chirped-Pulse Fourier Transform Spectroscopy Separate AWG Channels Generate Chirp Segments (Blue) and Local Oscillator (LO) Frequency (Red) with Phase Reproducibility Output Power: mW GHz GHz 260– 295 GHz 220 – 325 GHz WR 3.4 Low IF (720 – 1440 MHz) 4GS Digitizer

High Speed Segmented CP-FT Measurement Digitized at an IF of 720 – 1440 MHz at 4GS/s Real-Time signal averaging in 32 bit FPGA : sample memory (131 µs, at 4GS/s) 2 µs segments: µs chirped pulse µs decay time -720 MHz bandwidth (per segment) -50 segments (36 GHz, 100 µs )

Spectrum Relative Intensity Performance Frequency dependent spectrometer response: -Source power -Receiver mixer loss -IF amplifier gain -Propagation loss System response correction: -Routine response curve generated with series of stored single frequency waveforms -Correction incorporated into signal processing About 10-15% accuracy

Intensity Reproducibility Intensity variation < 0.1% Suitable for monitoring time evolution of the broadband spectrum

Comparison to Literature mm-wave Benchmark S. Fortman, I. Medvedev, C. Neese, F. De Lucia, ApJ, 725 (2010) 1682 CH 3 CH 2 CN 0.5 mTorr, 6 m path length, 24 s equivalent measurement time Speed: CP-FT is 10,000 times faster Intensity Accuracy: 15% vs. 1% (but 0.1% precision) Line width: 2.5 broader in CP-FT (magnitude FT + windowing)

High Dynamic Range Mode (HDR) HDR sequence: µs chirped pulse µs decay time -24 MHz bandwidth/seg -30 segments for each LO frequency (720mHz) -31 st segment for electrical background subtraction -50 LO frequencies (1500 total segments) 62  s for 720 MHz Two 720 MHz segments can be accommodated in the FPGA Noise Floor Achieved in 1s: 1  V (60,000:1 dynamic range)

Broadband Double Resonance Spectroscopy Acrolein Measurement Protocol: 1) Single Frequency Pump Pulse 2)720 MHz Chirp Observe ~60% signal modulation Sequential and V- Type Level Schemes Show Different Modulation Behavior

Conclusions 1)Real-time Signal Averaging is Achieved using Segmented Chirped Pulse Fourier Transform Spectroscopy 2)High Speed Mode Significantly Reduces Measurement Times Over Absorption Spectroscopy Methods 3)A High Dynamic Range Mode Provides Spurious Signal Reduction and Achieves about 100,000:1 (Largely) Spur Free Performance 4)Capabilities for Broadband Double Resonance Spectroscopy Can Translate Reduced Spectrum Acquisition Times to Reduced Spectrum Analysis Times Acknowledgments Brent Harris is supported by an NSF Graduate Fellowship University of Virginia Equipment Trust Fund NSF I-Corps