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Digital Holography

1.  Three-Dimensional Holographic Imaging of Multi-Phase Flows

Air bubbles in water-Tracking Animation

Fig 1-1: Left: Original hologram; Right: 3D reconstruction

Oil droplets in water -Tracking Animation

Fig 1-2: Left: Original hologram; Right: 3D reconstruction

References:

1. Lei Tian, Nick Loomis, José A. Domínguez-Caballero, and George Barbastathis, “Quantitative measurement of size and three-dimensional position of fast-moving bubbles in air-water mixture flows using digital holography,” Appl. Opt. 49, 1549-1554 (2010). pdf

2. L. Tian and G. Barbastathis, “Digital Holography Applied to Quantitative Measurement of Oil-Drop in Oil-Water Two-Phase Flows,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2010), paper DMC4.  pdf

2.   Three-Dimensional Holographic Imaging of Aquatic Species

The goal of this research project is to develop a Three-Dimensional Holographic Imaging system for aquatic species. The 3D Holographic camera will be carried inside an Underwater Autonomous Vehicle (UAV) that will be sent in an exploration mission to a depth of around 11,000 meters, currently the greatest depth attempted to image aquatic ecosystems. Figure 1 shows a sketch of a possible deployment.

Fig 2-1: Underwater holographic camera equipped on an AUV

Figure 2-2 shows the optical set-up for an experiment in the laboratory. The first target objects were brine shrimp swimming freely in a tank filled with seawater. Digital Holograms were created using a He-Ne laser (632.8nm) and a CCD camera KAF-16801E from Kodak. The CCD camera is a full-frame sensor with 4096×4096 pixels and a pixel size of 9 microns. A mechanical shutter controlled by a monostable multivibrator circuit synchronized with the CCD camera was used to set the integration time to 2ms.

Fig 2-2: Experimental setup

Figure 2-3 shows a typical hologram recorded using an in-line configuration with a plane reference-wave.

The following are some reconstructions of brine shrimp captured at short, medium and large distances from the CCD camera. The sampled brine shrimp ranged between 2-5mm in length.

References:

1. J. A. Dominguez-Caballero, N. Loomis, W. Li, Q. Hu, J. Milgram, G. Barbastathis, and C. Davis, ” Advances in Plankton Imaging Using Digital Holography,” in Computational Optical Sensing and Imaging (Optical Society of America, 2007), paper DMB5. pdf

2. J. A. Dominguez-Caballero, N. Loomis, G. Barbastathis, and J. Milgram, “Techniques Based on Digital Multiplexing Holography for Three-Dimensional Object Tracking,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2007), paper JThD84. pdf

Principle of Digital Holography

  • Digital holographic recording

The images are recorded in a high-resolution CCD/CMOS sensor using Digital Holography in a lens-free in-line configuration. The captured images (holograms) contain information about the phase and amplitude of the optical field propagated after illuminating the desired object. This information is encoded in the hologram as a set of fringes that are later decoded using image-processing algorithms to recover the intensity distribution at an image plane. This is located at a distance similar to the distance from the object to the camera. The typical in-line geometry is shown below.

Fig 3-1: Digital in-line holography geometry

In most of the experiments a plane-wave is used as a reference interfering with the field scattered by the object at the detector plane. The recorded intensity is then:

Where:

: is the reference wave
: is the object wave

If we expand this equation we get:

In this equation, the first two terms represent the so-called “DC term”, while the third and fourth term are the real and virtual images respectively.

  • Digital holographic reconstruction (Back-propagation method)

In order to recover the real image the first step is to multiply the above equation by a digital replica of the conjugate of the reference wave. In this step we are assuming that the effect of the DC term is weak so it can be neglected.

The virtual image is out-of-focus and, as shown in the experiments below, its effect for small objects at large distances is very small. For this reason it can also be neglected.

The second step in the back-propagation reconstruction algorithm is to apply a free-space propagation operation given by:

After paraxial approximations:

Where:

: is the reconstructed field at the image plane
is the wavelength used to record the hologram

is the transformation kernel and is given by:

The rest of the coordinates are shown in the following figure:

Fig 3-2: Coordinates in holography

The paraxial approximated transformation kernel has an analytic Fourier transform given by:

This allows us to implement the “convolution approach” for the reconstruction. In the convolution approach all the computations are made in the Fourier domain using the fast-Fourier-transform algorithms to make the reconstruction faster.  The block diagram followed for the case of in-line configuration with a plane reference wave is shown here.

Fig 3-3: Block diagram of digital back-propagation reconstruction

The dependence in distance of H allows us to “digitally scan” in the longitudinal direction. In other words, we can reconstruct the fields at different planes. In the case of two objects located at different distances from the camera, if we set the reconstruction distance equal to the distance from the first object to the detector plane, the second object will appear blurry while the first one will be in focus. Therefore, the 3D coordinates of an object can also be retrieved. The scanning process is exemplified in the following animation:

Fig 3-4: Digital backpropagation reconstruction

Click here to run animation

As explained above, we digitally scan for several reconstruction distances from a single hologram. An example of this procedure is shown in the movie below:

Click here to run the movie