Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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Advances in Optics, Photonics, Spectroscopy & Applications VI ISSN 1859 - 4271(a)(b)Fig. 1: modifications of the experimental setup from a single <strong>ph</strong>otodiode detector (a)to a CCD camera (b).III. RESULTS WITH A FAST CCD CAMERAThe fast CCD camera is a Photron Fastcam PCI that can take 1000 images/s. The frequencyof the wavelength modulation is f=500Hz.An example of recorded signal is presented on the following figure 2. The sheet of tracingpaper is very thin and the transit time through it is therefore negligible. We observe a time gatecentered at the time delay δτ between the two arms of the interferometer. Its width (FWHM) isthe time resolution of the setup: we measure, in this example, ∆τ ≈ 160 ps , in good agreementwith our theoretical expectations.(a)(b)Fig. 2: (a) the experimental setup for the measurement of a time gate.(b) Some example of the obtained time gateWe were unable to reach the expected SNR ratio, mostly for two reasons: first, these camerashave low quantum efficiencies, but the main problem is the high spatially correlated electronicnoise we found in the images (see figure 3).These cameras also suffer from other deficiencies, like a highly non-linear response or a veryslow sensor-to-computer data transfer rate. They are optimized for a very fast on-camera imagesequence recording of a single event, like crack propagation in a material sample or a car crashtest analysis.138
Những tiến bộ <strong>trong</strong> <strong>Quang</strong> học, <strong>Quang</strong> <strong>ph</strong>ổ và Ứng dụng VI ISSN 1859 - 4271Fig. 3: Fourier transform of an image. We see a lot of spatially correlated electronic noiseIV. RESULTS WITH A NORMAL CCD CAMERASo, we tried a normal CCD camera. Here, the tradeoff is very different from the previousexperiment: the CCD camera is a Hamamatsu C8484-05G, with 1.37 million pixels (i.e. aneffective pixel number equals to N≈0.8 million) for a frame rate ~9 images/s, and with quantumefficiency η ~ 25% @800nm.We use the diffraction order +1 of an acousto-optic modulator (AOM) in order to perform themultiplication by the positive function ξ(t). If i(t)≈i 0 +i int (t) is the <strong>ph</strong>otocurrent that a pixel shouldrecord without this modulation, then the charge stored in this pixel is:∫Q = ξ( t) i( t)dtWe will consider that for each acquisition frame the integral runs over only one modulationhalf-period. The <strong>ph</strong>otocurrent i 0 from the reference beam leads to a contribution Q 0 (with Q 0=g(0)i 0 T/2 ) while the <strong>ph</strong>otocurrent i int leads to the terms S DC (τ) and S DC (0). A time delay δτ =2060 ps is introduced between the two arms of the interferometer: transit times are thereforealways higher than this value, and the term S DC (0) can be neglected.As the reference beam illuminates the CCD sensor evenly, we should be able to cancel theterm Q 0 through a simple high-pass digital filter. The signal is however really low and evensmall heterogeneities on the acquired frame could lead to non-negligible components with highspatial frequencies. Therefore, we also perform the difference between two images (a) and (b) inorder to complete this cancellation and to leave only the S DC terms, which appear as a uniformwhite noise.∆ Q = Q( a ) ( b ) ( a ) ( ) ( b− Q ≈ S τ − S ) ( τ )The digital filtering also affects the signal and it can be shown that it reduces the effectivenumber of Fourier components, which is statistically equivalent to a reduction of the effectivepixels number that we estimated to be in the vicinity of a 58% reduction of the effective pixelsnumber. The time correlations we are going to consider in this paper are in the millisecondrange, so that there is no correlation between two successive frames. The variance of ∆Q is:22η eiη ei∆Q ≈ SDC4 f∫4 fDC2 02( τ ) = g ( 0) Π( τ −τ') φ( τ ') dτ' = g ( 0) Π * φ( τ )20DC139
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Nhng tin b trong Quang hc, Quang ph vÃ ng dng VI ISSN 1859 - 4271

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