Speckles are the result of interference of multiple randomly phased light waves. When the phases of these waves are modulated due to interaction of ultrasound with the medium, the intensity of the speckle is modulated. The modulation depth Iac is associated with the optical and acoustical properties at the location of the ultrasound and the local fluence. The light waves that cause the intensity modulation are said to be ‘tagged’ by the ultrasound. The associated intensity to this tagged light is It where the non-tagged light has an intensity of Int and the total light illuminating a CCD pixel n at time t can under assumption of the absence of higher harmonics be approximated by:
Where, , ω the ultrasound angular frequency and φ the random phase for pixel n, where for the time being we neglect higher harmonic signals. Here we want to demonstrate the use of a coherent ns pulsed laser in an AO application. We let this laser illuminate the scattering medium when a US burst reaches a region of interest inside that medium, at time t. A camera detects the generated speckle pattern I1 at the opposite end of the medium for which we write
A small time difference ∆t later a second laser pulse is injected in the sample. This time is chosen to be half the ultrasound period so that we have a phase shift of π. At that moment a second speckle pattern I2 is recorded, where:
Both speckle patterns are normalized such that the average intensity over all pixels is unity. The difference of the speckle patterns becomes larger if relatively more light has interaction with the US. We define the acousto-optic signal SAO that quantifies the amount of tagged light as
Where <> denotes averaging over all pixels of the speckle pattern. It can be shown that SAO
is proportional to the amount of tagged light by substituting Eqs. (2)
in Eq. (4)
and using the definition of Iac
. On substitution we obtain:
Hence the mean square difference of the speckle patterns is proportional to the amount of tagged light. Because of the normalization and we approximate . The proportionality constant is not important for a proof of concept because signal and noise are then multiplied with the same number.
This method has some similarities with an earlier technique that uses chopped CW lasers, which however needed orders of magnitude more camera integration time than the few nanoseconds that we use [7
7. S. Lévêque-Fort, “Three-dimensional acousto-optic imaging in biological tissues with parallel signal processing,” Appl. Opt. 40(7), 1029–1036 (2000). [CrossRef] [PubMed]
]. We will derive Eqs. (4)
in more detail in a later paper and make it quantitative instead of just qualitative. The difference between the two consecutive speckle patterns is caused by the effect of the ultrasound, speckle dynamics due to internal motion in the medium, camera noise and shot noise. By recording a large number of speckles (~105
) the noise is minimized and converges to a DC offset in the measured AO-signal. The DC component in the intensity of individual speckles cancels out.
Besides this difference-based method it is possible to include both light pulses in one camera exposure, which we refer to as the addition method. This results in one speckle pattern that is the sum of two instantaneous speckle patterns. This pattern has a contrast difference ∆C
compared to the contrast C0
of a speckle pattern of one pulse. For this implementation, the reduction in contrast is regarded as our acousto-optic signal. The reduction in contrast ΔC
is given by:
and the contrast of the integrated speckle pattern C is given by the standard deviation of the speckle pattern over its average value. For the sum of two speckle patterns this becomes:
This method is a variation of the speckle contrast method [8
8. J. Li, G. Ku, and L. V. Wang, “Ultrasound-modulated optical tomography of biological tissue by use of contrast of laser speckles,” Appl. Opt. 41(28), 6030–6035 (2002). [CrossRef] [PubMed]
] where we now use two short pulses of light instead of a continuous wave over an entire US cycle.
3. Materials and methods
For both types of signal generation we use the setup described in Fig. 1
Fig. 1 Experimental set-up. FG: function generators, AMP: amplifier, TR: Ultrasound transducer and BD: beam dump.
The novelty is the use of a highly coherent short pulse laser. We used a frequency doubled injection seeded Nd:YAG laser (Newport Quanta Ray lab series 170) with pulse repetition rate 10 Hz, and Fourier limited pulses with a duration of 5ns, which results in a coherence length of 1.5 m and a pulse energy of 350mJ. This system is capable of delivering enough light in a single pulse to generate a speckle pattern at the camera after transmission through a turbid medium and the energy is also sufficient for photoacoustic applications. Two synchronized function generators (FG)(Tektronix AFG 3102) give two TTL trigger signals for the laser consisting of flashlamp (FL) and Q-switch (QS) A third trigger is for the camera (CCD)(Allied Vision Technologies Manta G-145B NIR). At t = 0 the flashlamp is triggered, the QS trigger at t = 180 µs and the waveform for the US at ~162 µs depending on the depth of the ROI and the phase of the waveform. We use a simple setup for the delivery of the acoustics. The applied waveform is a sine at 5 MHz with 5 cycles. The waveform signal is amplified by ~50 dB by the amplifier (AMP) (Electronics & Innovation A075) and is connected to a focused 5 MHz US transducer (TR) (Olympus Panametrics-NDT V310). The laser light of 532 nm is attenuated with a half wave plate (λ/2) and a polarized beam splitter to reduce the pulse energy while operating the laser at its most stable settings. The excess light is collected by the beam dump (BD) so that the sample is illuminated with an optical pulse energy of approx. 3mJ. The repetition frequency of the laser is not high enough to give two pulses within one US cycle, thus we give a second US burst in time before the second laser pulse.
When the position of the US is shifted less than a wavelength the phase of the US is effectively changed. For the AO signal derived from the speckle pattern of two laser pulses the AO-signal strength depends on this phase difference. To show that the maximum signal is around π phase shift we perform a phase stepping experiment where we find the signal strength as function of the phase difference of the US bursts. Maintaining a π phase shift of the US between the two pulses of the laser it is possible to obtain an image by scanning the US focus through the object. We only use two phases for several reasons. Firstly it keeps the measurement time limited. But more importantly, in the eventual implementation we are will deliver 2 laser pulses within one US cycle, the current two phase measurement mimics this as close as possible. For the time being we need an object with tissue like properties with a longer speckle decorrelation time to overcome the problem of a low repetition rate of the laser. The phantom is a cylinder with a diameter of 20 mm and a length of 40 mm consisting of 3% agar and 3% Intralipid 20% without added background absorption. The background reduced scattering coefficient is estimated to be µs’ = 0.6 mm−1. We scanned in the plane perpendicular to the ultrasound propagation direction, which is in z direction. The optical axis runs parallel to the y-axis. The optodes at the opposite ends have a diameter of 3mm. Both the subtraction and addition method were applied at the same time from the same speckle patterns. For the addition method we need to determine C0 for every data point, however this contrast value remains the same within a small variation during the whole experiment. Therefore we assume this value to be constant and it is only measured at the start of the experiment.
We performed a measurement on the same phantom in an acousto-optic setup based on speckle contrast and a CW laser with the same experimental settings. Only the integration time of the camera is enlarged to 10 ms per speckle pattern to capture enough light, opposed to the effective 2 phases times 5ns = 10 ns integration time in our novel method. We chopped the light from a CW laser (Coherent Verdi 6, 532nm) with the use of an acousto-optic modulator to obtain pulses of 1 µs. So we only tag light from the same region as in the other experiments. Within the 10 ms exposure time we send 250 acoustic and laser pulses to capture enough light. At the opposite end of the object we capture a speckle pattern with the camera. In this way we show the relation between AO-signals generated with the speckle contrast method and the proposed technique.
But before these experiments we performed a stroboscopic measurement on a very stable phantom to test the setup. With our system we obtained snapshots of a speckle pattern for different positions of the ultrasound. By varying the delay between light and sound delivery we stroboscopically recorded the evolution of the speckle pattern while the US travels through the medium. The ultrasound traveled along the z-axis and we placed the origin of this axis at the US focus. This experiment took several minutes and we wanted the speckle pattern to return to its original shape. This required a very stable sample material. We performed this experiment with a very stable homogeneous 5% agar phantom with paper particles of size ~300 µm as scatterers. The dimensions where the same as previously described phantom. We used the bigger paper particles in a more rigid agar matrix to maximize the decorrelation time of the speckle pattern. Brownian motion and thus speckle decorrelation is particle size dependent and the bigger scatterers result in the sample result in a decorrelation time of 10 minutes (speckle pattern cross correlation reduced to ~90%).
5. Discussion and conclusions
The above experiments show that it is possible to obtain AO-signals with a ns pulsed laser. For this we used an injection seeded Nd:YAG laser with Fourier limited pulse, implying a coherence length of 1.5 m. First of all, with the used laser it is possible to generate speckles through a 2 cm thick scattering sample with a contrast of 0.43 when both polarizations are allowed on the camera. This implies that the coherence length of the pulsed laser is sufficient. The stroboscopic measurement (Fig. 2
) also shows that pulse to pulse no big mode hops or other beam instabilities are observed that would lead to different speckle patterns between pulses. All the speckle patterns for which no US is applied are virtually the same. We see that both bright and dark speckles contribute to the AO-signal, and that the bright speckles show more modulation (Fig. 2(a)
). The relative amount of higher harmonics in the speckle intensity modulation depends on the brightness as well (Fig. 2(c)
). This can be understood by taking the extreme case of a zero intensity region in the speckle pattern due to destructive interference: a modulation of part of the light by frequency ω will result in a 2ω frequency of the associated intensity variation since during each US cycle the local intensity will go from a minimum value (zero) to a maximum value twice. On the other hand, the brightest observed speckle is far from the maximum brightness possible, since in that case all the available energy goes into this single speckle, leaving the rest of space dark. And it is only this maximum possible intensity speckle that only can become less bright and might give higher harmonics.
The AO-signal strength depends on the US phase difference between the moments of illumination of the sample by the laser pulses. The maximum AO-signal is obtained for a phase shift of π radians. (Fig. 3
) The phase stepping experiment also shows that the shift of the US pulse over 2π or 1 US cycle brings the AO-signal close to that of the 0 shift case but not entirely. This is because the shifted US burst which consists of 5 cycles only overlaps for 4 cycles with the original one. However this effect is small enough to be neglected when performing a scan.
The AO-signal strength as defined by Eqs. (4)
behaves spatially very similar to speckle contrast measurements as shown by the scans for both the subtraction as addition method. (Fig. 4
) Both results obtained with the pulsed light are spatially very similar (Fig. 4(a)
). As for their quantitative agreement, in a pixel-by-pixel comparison we observe on average a factor of ~4.8 between the results of the two methods. (Fig. 5
) These scans are also similar compared with the speckle contrast method. (Fig. 4(c)
). A part of the ‘noise’ in Fig. 5(a)
is caused by the slight tilt in the scan of Fig. 4(c)
The equivalence of results after addition or subtraction of speckle patterns initially is counter-intuitive but can be explained. (Fig. 5(b)
) The bigger the difference between speckle patterns and keeping the average intensity constant for both would result in a lower standard deviation and thus lower contrast value. The fact that the addition method scales linearly with the difference method brings a great opportunity. For in-vivo applications an AO-signal should be acquired within the speckle decorrelation time of less than 0.1ms. Using two laser pulses within one US period can prevent speckle decorrelation within a measurement, e.g. a time interval of 100 ns between the two pulses for a 5 MHz US burst. To temporally resolve the speckle patterns resulting from these two pulses an ultra high-speed camera or a correctly triggered camera with sufficient short dead time is needed with high enough resolution for averaging over speckles. These cameras are expensive and large making them less desirable for future application. The addition method is equivalent to letting the camera integrate over two laser pulses. In the case of the addition method a relatively cheap and slow camera system can be used even in the case when much higher US frequencies are used and thus much shorter time between laser pulses. We see this as an important step towards in-vivo applications. To make this work we need to inject two laser pulses with sufficient wavefront matching, e.g. by splitting off light to a properly designed optical delay line. The properties of the used laser such as pulse duration and energy enable a combined performance of acousto-optic and photoacoustic measurements.
We acknowledge Berkan Basel and Ivo Vellekoop for their work that resulted in the stroboscopic speckle movie.
This work is performed by the Foundation for Fundamental Research on Matter (FOM) under grant 09NIG01, which is part of the Netherlands Organization for Scientific Research (NWO).
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