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Speckle imaging was investigated by using dynamic holography and photorefractive AlGaAs/GaAs multiple quantum wells in a holographic optical imaging system. We showed that the speckle contrast depends on holographic fringes and the photorefractive effect. We further demonstrated that a moving grating technique can be used to suppress the random speckle.
©2007 Optical Society of America
1. Introduction
Holographic optical imaging technique using photorefractive multiple quantum wells (PRQW) has shown great potential in biomedical imaging applications, such as laser based ultrasound detection [1–4], adaptive optical coherence domain reflectometry (OCDR) [5,6] and holographic optical coherence imaging (OCI) [7–11]. In laser based ultrasound detection and adaptive OCDR, PRQW acts as a dynamic beam combiner in an interferometer. Photorefractive phase of the PRQW locks the ultrasound signals at the quadrature (90° phase difference between the signal and the reference) while low frequency laser speckle and environment vibrations are compensated by dynamic holograms [1]. By using the PRQW, weak ultrasound signals are effectively detected through a turbid medium [2]. In holographic OCI, coherent images are recorded in PRQW through dynamic holograms. The adaptive capability of the hologram has been used to overcome the interferometric instability when imaging through a biological tissue [9–11]. Multiple quantum wells have also been used as spatial modulators in a speckle photography [12,13]. In all of those applications, speckle images are strongly influenced by holographic fringes as well as photorefractive effect. The PRQW has been used to reject unwanted speckle in some applications, such as laser based ultrasound detection. On the other hand, it has been used to acquire useful speckle images in other applications. For example, dynamic speckle in holographic coherence domain imaging has been applied to analyze the cellular movement and healthy state of a tumor tissue [11]. Despite the speckle plays an important role in holographic optical imaging, the mechanism underlying the speckle imaging is still not clear.
In holographic optical imaging using PRQW, numerical aperture (NA) of the detection is large compared to other coherence domain imaging technique, such as optical coherence tomography. The large NA is required by the field of view in the imaging system, which is related to the device window size. Light photons from a large angle scattering are collected so that the size of speckle pattern is comparable to the fringe spacing of the interference. Therefore, the holographic grating formed in the PRQW can be used to select and manipulate speckle patterns. In this paper, we provide the first study for the contrast mechanism of speckle imaging in the holographic optical imaging using AlGaAs/GaAs PRQW. A cw laser is used as the light source to provide well controlled speckle patterns. Furthermore, a moving grating technique is proposed to suppress the speckle.
2. Experiments
Our experimental imaging system consists of a Mach-Zehnder interferometer, an AlGaAs/GaAs PRQW device served as a holographic record medium, and a CCD camera (SONY, SPT-M124) as illustrated in Fig. 1. A 4-F lens pair relays the image from the object plane (the sample plane) to the image plane (the device plane). A non-degenerate four-wave mixing (FWM) is used to record and reconstruct holograms. A cw He-Ne laser (632.8nm, 10 mW) serves as the light source. The signal beam and the reference beam cross a small angle to generate fringes in the PRQW. A laser diode (Hitachi DL5032) is used as the probe beam. The wavelength of the diode laser is tuned to the excitonic peak of the device.
Speckle patterns are generated by light shape diffusers (Newport Cooperation) [14] placed on the object plane of the imaging system. The light shape diffusers have various diffusion angles and light can be shaped into these specific angles. An aperture is placed between the diffuser and the lens. The aperture is used to limit the collecting angle.
3. Results and discussion:
1. Speckle imaging
To investigate speckle imaging we recorded two kinds of speckle patterns at the device location: direct speckle images and holographic speckle images. Direct speckle images are acquired by blocking the reference beam in the interferometer, as shown in Fig. 2(a). The sharp edge of the speckle image originates from the 1 mm window of the PRQW device. Average speckle sizes along horizontal direction and vertical direction of the image are calculated according to the autocovariance function [15], as shown in Fig. 2(b) and Fig. 2(c).
Holographic speckle images (Fig. 3(a)) are reconstructed by using a probe beam in a non-degenerate four-wave mixing. The baseline variation in Fig. 3(b) is due to the autocorrelation of the device window. The baseline variation is small in Fig. 3(c) since the device window is larger than the beam size in the vertical direction. As shown in Fig. 3, the holographic speckle has a difference size and intensity distribution compared to the direct speckle image.
Since the speckle is modified by the holographic process in the PRQW, the statistics of the speckle is related to the intensity level of the probe beam and the intensity ratio between the signal and the reference. To avoid the intensity issue we use a threshold or clipped method to analyze the intensity statistics of the speckle [16–18]. The histogram of the speckle image gives the intensity range of the image. Within this intensity range, a series of specific threshold values are selected. The total bright pixels with their intensity above the threshold are counted. The average speckle area of the clipped speckle is calculated by dividing the pixel number of the speckle above the threshold level to the total pixel number. The result indicates that the average speckle area is decreased with the increase of the intensity threshold, as shown in Fig. 4(a) and (b).
Fig. 4. Comparison of theoretical predictions with experimental measurements. (a) Direct speckle image, (b) Holographic speckle image.
Based on the speckle theory [19], the statistics of the speckle can be understood by examining the gamma probability density function (PDF). The average speckle area that can be predicted theoretically is a function of three parameters [17,19]: (1) It/Ia where It is the preset threshold intensity and Ia is the mean intensity of the image, (2) the shaping constant of the gamma PDF, M, which is equal to (Ia/σI) 2 where σI is the variance of the intensity, and (3) the second moment of the normalized power spectral density of the field, l, which is resulted from the peak curvature of the normalized autocovariance function. The histogram of the direct speckle image gives a mean intensity of 76.93 and a variance of the intensity variations of 53.55. The shaping constant of the direct speckle image is calculated to be 2.064. In our case, the surface roughness of the 10° diffuser is on the scale of the wavelength. The intensity distribution of the direct speckle image comes from the sum of two unpolarized intensity distributions so that the shaping constant of the gamma PDF should be 2. This value is very close to the experimental result. Using experimental parameters of the holographic speckle the shaping constant is calculated to be 0.74. In general, a fully developed speckle from a sum of a random phasor and a constant phasor gives a shaping constant of 1 in a negatively exponential gamma PDF. In holographic optical imaging, the speckle is modified by the reference that is coherent to the signal. Further contrast modification of the speckle comes from the nonlinear response of the holographic grating to the interference fringes, the intensity level of the probe beam, and the dynamic range of the photorefractive effect. Based on experimental parameters from both speckle images, theoretical calculations based on the gamma PDF give a good consistency to the experimental results, as shown in fig. 4(a) and (b).
2. Speckle size and four-wave mixing
In a holographic optical imaging system the FWM efficiency is a function of the fringe spacing. Since interference fringes are involved in the formation of the holographic speckle, the FWM efficiency is also a function of the speckle size. On the other hand, FWM can determine how the speckle is imaged through the photorefractive effect. Here we demonstrate this influence by examining the FWM efficiency as a function of the fringe spacing and the speckle size.
The speckle size of the direct speckle image is calculated according to the autocovariance function, as shown in the section 1. The fringe spacing is defined by the crossing angle between the signal and the reference, which is given by
where θ is the half-angle between the beams and λ is the wavelength. In PRQW the third-order optical nonlinearity is based on the Franz-Keldysh excitonic electroabsorption when an electric field is applied to the PRQW device in a transverse-field geometry [20]. The periodic intensity modulation introduces two gratings, absorption grating and refractive index grating with photorefractive phase shifts in the PRQW. The diffraction efficiency can be described by using these two gratings. The photorefractive gratings diffract the probe beam and the holograms are reconstructed by using the non-degenerate FWM in the PRQW.
FWM signals are collected by using a lock-in amplifier while the probe beam is chopped. The first-order diffraction of the probe beam is recorded by a photodiode and the zeroth-order is blocked by a rectangular aperture. The FWM efficiency as a function of the fringe spacing is shown in Fig. 5(a). Under a uniform illumination, the FWM efficiency decreases with the decrease of the fringe spacing, and then drops off rapidly at the fringe spacing below 5 µm. For the speckle imaging, the maximum FWM efficiency occurs at the fringe spacing about half size of the speckle. Relationship between the FWM efficiency and the speckle size is shown in Fig. 5(b) at a fringe spacing of 17 µm. Variable speckle sizes are achieved by changing the aperture size of the 15° and 25° diffusers. In Fig. 5(b), the FWM efficiency decreases sharply when the speckle size is smaller than the fringe spacing. For the 15° diffuser, the FWM efficiency shows flat dependence as a function of speckle size near the fringe spacing, and then decreases slowly when the speckle size is above 25 µm.
The dependence of FWM efficiency as a function of the fringe spacing has been described by the transport effect of the photocarriers in the PRQW [20]. Additional FWM efficiency decrease in the speckle field when the speckle size is smaller than the fringe spacing can be understood by the phase characteristics of the speckle and the coherence of holography. In this case, no interference fringe can be formed in the holographic medium due to the random phase of the speckle. If the size of speckle is much larger than the fringe spacing, the effect of the speckle on the fringes will cause shifting and bending by a random length due to the random phase of the speckle. Therefore the FWM efficiency decreases as the speckle size increases.
3. Moving grating technique
From previous section we can see that the FWM efficiency has the highest value when the speckle size is twice of the fringe spacing. The holographic speckle should have the highest contrast at this size range. Since the fringe spacing is roughly equal to the resolution of the holographic imaging system, the presence of the holographic speckle can strongly degrade the image quality, as demonstrated in Fig. 6(a) and (b).
Fig. 6. Comparison of holographic images of USAF test chart without moving grating ((a) and (b)) and with moving grating ((c) and (d)). (e) Simulation of speckle intensities with and without moving grating.
We propose a moving grating technique to solve this problem. A mirror in the reference arm of the interferometer is vibrated at a frequency of 600 Hz by using a piezoelectric stack. This results the same-frequency vibration of fringes inside the PRQW. The PRQW has a fast response time (about 100 KHz at an intensity of 100 mW/cm2) so that it can track the moving grating. The frequency of the vibration is sufficiently high to allow the CCD camera to take a time average over many cycles. The difference in response times between the holographic record medium and CCD camera allows the system to average the speckle while retaining the full spatial coherence and intensity variation arising from the structures in the sample. The phenomenon is similar to the speckle suppression technique of moving screen in projection displays [19]. As shown in Fig. 6(c) and (d), the function of the moving grating technique for reducing the noise speckle is apparent by comparing the holograms of number three and bars in the group four of a USAF test chart with and without vibration. Fig. 6(e) gives a simulation on the holographic speckle intensities with and without vibration. The vibration frequency of the moving grating is 600 Hz. The integration time of the CCD camera is set to be 30 ms. Based on the simulation, it is apparent that the holographic speckle intensity with 600 Hz vibration decreases to about 1/4 of the holographic speckle intensity without moving grating.
4. Conclusions
In conclusion, we analyzed the speckle statistics in holographic optical imaging using PRQW. Theoretical prediction of the speckle gamma PDF shows a good consistency to the experimental results. We systematically studied the relationship among the speckle size, the fringe spacing and the FWM efficiency. The FWM efficiency drops sharply when the speckle size become smaller than the fringe spacing and decreases slowly when the speckle size is larger than the fringe spacing. Furthermore, we presented an efficient method to suppress the speckle by using a moving grating technique.
Acknowledgements
The authors would like to thank David Nolte for providing the devices. This work was supported by the University of Missouri Research Board Grant URB-04-072.
References and links
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