The controlled interference between two short pulse lasers has recently been used for a variety of applications from spectroscopy to reflectometry [1
1. F. Keilmann, C. Gohle, and R. Holzwarth, “Time-domain mid-infrared frequency-comb spectrometer,” Opt. Lett. 29, 1542–1544 (2004). [CrossRef] [PubMed]
2. I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent Multiheterodyne Spectroscopy Using Stabilized Optical Frequency Combs,” Phys. Rev. Lett. 100, 013,902 1–4 (2008). [CrossRef]
3. P. Giaccari, J.-D. Deschênes, P. Saucier, J. Genest, and P. Tremblay, “Active Fourier-transform spectroscopy combining the direct RF beating of two fiber-based mode-locked lasers with a novel referencing method,” Opt. Express 16, 4347–4365 (2008). [CrossRef] [PubMed]
]. Coherent laser detection and ranging (LADAR) application has even been demonstrated and proposed to control the attitude of spacecraft constellations [4
4. I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nature Photonics 3, 351–356 (2009). [CrossRef]
]. In this scheme, a frequency comb probing the target is combined at the receiver with a second, slightly detuned, comb to measure the optical delay interferometrically. A similar scheme was also proposed with a mode-locked laser and an interferometer [5
5. M. Cui, M. G. Zeitouny, N. Bhattacharya, S. A. van den Berg, H. P. Urbach, and J. J. M. Braat, “High-accuracy long-distance measurements in air with a frequency comb laser,” Opt. Lett. 34, 1982–1984 (2009). [CrossRef] [PubMed]
], the distance being found from the cross-correlation between pulses performed by the interferometer.
For remote sensing applications where the sources are uncooperative (e.g a diffuse reflector), the coherent approach can be problematic because of the fading arising from the fact that the wavefront returned by the target is distorted with respect to the reference beam.
In this paper, we propose to probe the scene with two slightly detuned combs. The two combs can be either distinct lasers, or generated with a single short-pulse laser and an interferometer, the latter being done in the paper. The ranging information is retrieved from the time-of-flight, much like conventionnal laser range finders. The interferometer is used to modulate the beam such that, after a Fourier transformation, a ranging trace can be obtained for each spectral component of the source, at high spectral resolution. This can thus be called spectrally resolved optical ranging.
2. Increasing the spatial range
A Menlo Systems C-comb mode-locked laser, with repetition rate and carrier envelope offset (CEO) controls is used to carry the demonstration of the spectrally resolved ranging scheme proposed here. The repetition rate of the laser is set to 100 MHz. In free space the distance between two successive pulses is thus 3 m. This gives a round-trip non-ambiguous range of 1.5 m. When measuring the time-of-flight, it is indeed impossible to distinguish between a pulse going to N × 1.5 m and back from the N-th successive pulse going to only 1.5 m.
Pseudo-random binary modulation of the pulses to increase the non-ambiguous range. PC stands for polarization controller. The pulse generator conditions the electrical pulse train issued by the detector. The Bit Error Rate Test Set (BERT) generates the wanted PRBS. Full setup, with interferometer and telescope is provided on Fig. 4
Increasing the non-ambiguous range by a factor N
can of course be achieved with a pulse picker, by keeping only one pulse in N and thus reducing the repetition rate by a factor N
. To be compatible with the rapid-scan interferometer used to generate the second comb, a high pulse rate is however needed. To acheive this, the output of the pulsed laser is modulated by a synchronized pseudo-random bit sequence (PRBS), as shown in Fig. 1
A small fraction of the optical signal is used to clock an Anritsu ME522 telecom analyzer generating a selectable length PRBS. The PRBS is seeded to the pulse picker (an E/O Space electro-optic intensity modulator). The expanded non-ambiguous range becomes limited by the duration of the sequence, which is N times the laser repetition period. On average only one pulse out of two is dropped so the power penalty of the approach is a only factor two, regardless of the sequence length.
The approach is similar to the use of a modulator with continuous wave (CW) lasers for ranging [6
6. C. Nagasawa, M. Abo, H. Yamamoto, and O. Uchino, “Random modulation cw lidar using new random sequence,” Appl. Opt. 29, 1466–1470 (1990). [CrossRef] [PubMed]
]. The difference is that in the scheme described here, the speed of the modulator does not limit the spatial resolution, because it is used only to gate the pulses.
For the sequences shown in Fig. 2
, a specular reflector has first been placed at 4.2 m from the telescope, to provide a distance reference. The blue trace is the sequence measured with the reference reflector. A diffusely reflective target is then placed further, at 12.2 m from reference reflector and the sequence shown in red was measured. The distance between the two reflectors was chosen to be close to eight times the original non-ambiguous range. On Fig. 2
individual pulses nearly superimpose, but it is quite obvious that there is a delay between the two sequences.
Fig. 2. Two sequences corresponding to a relative distance of 12:2 m. Blue: Reference specular reflector at 4:2 m, Red: Diffuse reflector at 16 m. Matching the sequence patterns allows to increase the non-ambiguous range.
A circular correlation between the sequences reveals the LIDAR trace for the full range corresponding to the chosen sequence length. Figure 3
shows such a trace for a specular reflector located at 10.5 m compared to our reference. In this case, the sequence length was 127, so that the expanded non-ambiguous range is 190.5 m.
Maximal length pseudo-random sequences are used because of their correlation properties. The autocorrelation of a bipolar maximal length PRBS is such that it is equal to N
, the sequence length, for zero delay and to −1 for all other delays [7
7. S. W. Golomb and G. Gong, Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar, 1st ed. (Cambridge University press, 2005). [CrossRef]
]. Denoting the bipolar sequence M
] one can write:
where ⊗ denotes the circular correlation.
where Γ is the received power and the transformation is just to make S[n] unipolar.
Fig. 3. A circular cross-correlation between the received trace and the sent (or reference) sequence yields a ranging trace over an expanded non-ambiguous range of 190:5 m, specular reflector at 10:5 m.
The correlation performed to retrieve the ranging trace on the expanded non-ambiguous range is:
Again using the correlation properties of the maximal length PRBS M[n], the correlation with one is the sum of the sequence, which is −1. One can therefore write:
The peak amplitude, corresponding to the location of a reflecting event, after correlation is thus Γ(N
−1)/2. All other delays yield a correlation equal to −Γ. The dynamic range limitation is therefore (N
−1)/2 on each acquired trace. The structure seen on the floor of Fig. 3
is actually this limit, which is 63 for a short sequence of length 127, yielding a 10*log10(63) = 18 dB dynamic range.
3. Generation of the second comb and complete setup
The setup to perform spectrally resolved ranging is shown in Fig. 4
. The pulses are first stretched by a 200 m spool of SMF-28 fiber. This is done before amplification to limit the peak power and stay in a linear regime in the fiber after the amplifiers. The amplification chain consists of an INO (FAD model) pre-amplifier followed by a Pritel HPPFA-33, high peak power amplifier. The maximal ratings of this amplifier are 2.5 W of continuous power and 4 kW of peak power before pulse breaking occurs.
Fig. 4. Complete setup for spectrally resolved ranging system. A comb is modulated by a maximal length PRBS sequence. The pulses are then stretched with SMF fiber and amplified. A reference sequence is recorded before final amplification, collimation (B. Ex. stands for Beam expander) and interferometric modulation. Optical signals are represented with thick lines, electrical signals with thin lines.
A fiber coupler collects 2% of the power after the first amplifier. This provides the reference sequence. Any measured distance will therefore include the fiber length in the second amplifier. This is easily calibrated by putting a reference reflector at a known distance in front of the telescope, as done in section 2, for the result presented in Fig. 2
The output of the high power amplifier is sent to a beam expander producing beam with a 2.4 cm waist diameter. The waist is experimentally placed 151 m away. Reflexions from the targets are collected with a 6 inch, f-5 telescope.
A 1 GHz detector (New Focus 1611-FS) is placed in the focal plane and the electrical signal is amplified with a 700 MHz pulse amplifier having 30 dB of gain (Mini Circuits ZPUL-30P). The acquisition is performed, at 5 G samples per second, with a Lecroy Wavepro 7 Zi oscilloscope having an acquisition memory of 32 M points per channel. The spatial resolution is therefore 21 cm and the spatial sampling is 3 cm.
In this paper, to demonstrate the principle, the two sliding combs are generated using a Michelson interferometer. The output of the beam expander is sent through the interferometer, so that pairs of pulses with varying time delays are sent to the target. The idea is to acquire one pseudo random sequence (hence a complete range scan) for each optical path difference (OPD), produced by the interferometer.
A 632.8 nm HeNe laser is measuring the optical path difference of the interferometer. A trigger event is produced at each rising fringe of the reference laser interferogram. A total of 6350 samples at 5 GHz are acquired at each trigger event. This way, one pseudo random sequence is acquired after each of the 1500 trigger events around the zero path difference of the interferometer.
The interferometer scans slowly so that the OPD change during one sequence is smaller than 1/1000-th of a fringe at 1550 nm. The interferometer speed is set such that the 632.8 nm HeNe fringes produce a 2 kHz signal. Measurements therefore last 750 ms (1500 fringes at 2 kHz). However, since only 1500 × 6350 samples are taken, the signal observation time is actually 1.9 ms during each measurement.
Fig. 5. Modulated cross-correlated pulses yield interferograms at increasing distances. One interferogram is measured for each 3 cm spatial depth. Spatial resolution is however 21 cm. Specular reflector located at 6.4 m. The optical path difference scale is on 632.8 nm fringes
After cross-correlating each sequence with the reference trace, one obtains an interferogram for each distance within the expanded non-ambiguous range. This is illustrated in Fig. 5
, where a specular reflector was placed at 6.4 m to align the system. An equivalent way of seeing this is that a ranging trace is measured for each optical path difference of the interferometer.
The maximal path delay of the interferometer fixes the spectral resolution, which is 10 cm−1. The interferometer used was able to scan longer delays but measurements were limited by the memory of the oscilloscope.
At 10 cm−1, the maximal spatial separation of the pulses in a pair is smaller than 500 µm, (or 1.6 ns). This separation does not affect the ranging experiment which has a spatial resolution orders of magnitude larger. The impulse response of the detector therefore still dominates the instrumental response of the ranger. The only difference is that the amplitude of the pulses is temporally modulated by the inteferometer. This modulation carries the spectral information. The spectral and spatial dimensions are therefore acquired independently, e.g without appreciable cross-talk.
Taking the Fourier transform along the interferometry dimension gives the spectrally resolved ranging information, as shown in Fig. 6
. Two interesting features are visible on this figure. First, the spectrum reflected by the target is clearly visible at the expected distance. Figure 7
shows the spectrum measured in the slice at 6.4 m, in which the characteristic shape of our amplified mode-locked laser is apparent. Second, a line can be seen on Fig. 6
for all distances within the spectral range of the source, that is around 6400 wavenumbers. Figure 8
shows the ranging information at 6415 cm−1
where the peak amplitude has been normalized to 0 dB. The structure seen at around −18 dB arises from the limit on the dynamic range set by the correlation and the sequence length.
Fig. 6. Spectrally resolved ranging trace, with a specular reflector at 6.4 m. One spectrum is obtained for each 3 cm spatial depth. The spatial resolution is 21 cm. Signal to noise limitation is seen in the spectrum at the reflector distance (6.4 m) while dynamic range limitation due to the cross-correlation is seen for all distances at the wavenumber having the peak signal (6415 cm−1). More details on the two next figures.
Slice of Fig. 6
showing the spectrum reflected at 6.4 m, the target distance. Spectral resolution is 10 cm−1
Slice of Fig. 6
showing the ranging information at the peak signal wavenumber (6415 cm−1
). The structured noise floor is arising from the cross-correlation dynamic range limitation: 10*log10[(N-1)/2] = 18 dB, with N=127. Spatial resolution is 21 cm.
4. Averaging traces
Measurements of several paint samples provided by DRDC Valcartier were carried and single pulse detection was possible at up to 16 meters with nearly all the samples. To increase the ranging distance, or the spectral signal to noise ratio, several measurements can be averaged. Except for the fact that this represent a significant data set, the task is pretty straightforward. One example of the results obtained is shown in figure 9
, in which 1000 spectrally resolved ranging measurements were averaged for one of the paint samples.
This paper proposes an approach to perform spectrally resolved ranging. The approach can be implemented with one pulsed laser and one interferometer or by carrying interferometry between two modelocked lasers. The paper demonstrate experimentally all the concepts and spectra are retrieved from targets at short distances, showing that everything works as expected.
Two factors currently limit the approach and they are linked one to the other. First, the source used in our demonstration does not have enough energy per pulse to retrieve ranging information on long distances. This is not a fundamental limitation. The pulse rate could be decreased before amplification. With a final amplification stage able to sustain the same average power for the lower repetition rate, such as commercial LIDAR amplifiers, and with proper pulse width management, it can be expected that the pulse energy and thus the signal to noise ratio or ranging distance can significantly be increased to reach performances comparable with current LIDARs at 1550 nm. With a lower pulse repetition rate, it will probably be wiser to adopt a step-scan approach either with the interferometer or with the second laser.
The second issue is the spectral width of the source and of the amplifiers. This width obviously limits the range onto which we can retrieve spectral information from the targets. Modelocked lasers typically exhibit a 100 nm bandwidth around 1550 nm, with amplifiers decreasing this down to 50 nm, depending upon the gain applied. The bandwidth of the amplifier is thus an important parameter. One can of course think of broadening the spectrum with non-linear optical elements after the last amplifying stage. It is believed that this issue will require significant work, especially for the dual laser approach in which the coherence and the comb nature of the sources must be maintained.
Fig. 9. Average of 1000 spectra reflected by a diffuse target at 6.4 m, spatial resolution is 21 cm, spectral resolution 10 cm−1.