Common optics obtain quadrature images

An imaging method that obtains both amplitude and phase information from an object in the field of view is based on a common Mach-Zehnder interferometer and several polarizers. Quadrature imaging was developed by Daniel Hogenboom, Charles DiMarzio, and others at Northeastern University (Boston, MA) and provides information in a single measurement that can be used to construct a three-dimensional (3-D) image. Because the method is scalable, explains postdoctoral researcher Hogenboom, it has applications ranging from microscopy to Doppler laser radar.

Quadrature imaging in radar applications is achieved by mixing the signal with an in-phase reference (a cosine wave) and a quadrature reference (a sine wave) that is 90° out of phase with the cosine wave. Dimarzio explains, "The resulting mixer outputs contain the real and imaginary components [that is, the amplitude and phase] of the complex signal." The method uses a circularly polarized reference to give back the sine and cosine at the same time, one in each polarization, resulting in four images at the output plane.

Holography also obtains phase information, but the hologram created by mixing reference and signal beams can be contaminated by a ghost image formed because the hologram records only the magnitude of the optical field. Quadrature imaging allows the complete field to be retrieved.

The laser beam in one arm of the Mach-Zehnder interferometer—the signal beam—is linearly polarized at 45° to vertical, and the object being viewed is placed in this path. The reference beam is circularly polarized using a quarter-wave plate; the beams are combined, and they pass through a polarizer in front of a CCD camera. Rotating the polarizer from vertical to horizontal alters the interference pattern, providing both image intensity and phase information.

The method can be used for diffraction tomography: the interferogram provides enough information to permit an accurate reconstruction of the original object. In one experiment, a pair of small slits was used as the object, creating a diffraction pattern that was captured in the far field. An image was reconstructed using the Fresnel integral. The horizontal resolution of the slit widths and spacing (FWHM) agreed to within a few percent with measurements of the slits. The slits are not fully resolved due to the limited size of the CCD array. The depth of field is proportional to the square of the distance to the object and inversely proportional to the square of the width of the array.

Extracting the image from the interferogram involves calculating the Fresnel integral, which requires the researchers to input the distance from the detector plane to the object. With 3-D objects, the distance can be varied to create a series of images, much like changing the focus of a microscope to observe different depths. Algorithms designed for optical tomography can be applied to these quadrature images. Information on all the planes in the object is obtained at the same time.

A further refinement of the system removes the need for a moving polarizer in front of the camera. After the reference and signal beams are recombined, polarizing beamsplitters separate the polarizations. This makes it possible to obtain all four interferograms required for processing at once, with no moving parts in the system.

Applications

The device is still in the development stage, although the researchers are considering various applications for imaging objects that do not depolarize or diffuse the laser light. With a microscope and a scanning focused source, quadrature imaging could provide a complete 3-D image for each position of the light source. Three-dimensional imaging and spectroscopic information could be obtained simultaneously by using a source with several output wavelengths, along with appropriate filters and cameras. Use of multiple wavelengths with quadrature imaging could provide 3-D spectral information.

The quadrature imaging concept has been used by researchers for Doppler lidar, allowing them to determine in which direction an object is moving—approaching or receding—in a single measurement, instead of merely its speed. Future work, says DiMarzio, will focus on reflective imaging.