Fourier Holographic Angular Scattering Spectroscopy

Fourier holography

As mentioned in the Introduction to holography, Fourier holography, in combination with digital imaging and post processing has become a promising and powerful technique. Research at OBEL focuses on methods of inspecting the morphology and microscopic features of biological samples over a very large field of view with a single image capture. Detection of dysplasia in cells (abnormal shape) as a means of cancer diagnosis is an example of how this information could be used. Current methods involve investigation of tissue under a microscope and are rather laborious and time consuming. For sufficient magnification and resolution the investigated area becomes quite small and thus requires several microscopic images to be taken. Our technique could overcome these limitations by capturing the microscopic information over a large area in a single image.
Figure 1 shows a configuration for a setup which is currently used in one of our labs.

Fourier holography setup
Figure 1. Off-axis Fourier holography setup with the reference arm (top) and the sample arm (bottom); the sample is shown enlarged at right.

Fourier holography is a type of holography in which the interference pattern between the Fourier transform of the object and a plane reference wave is recorded. In our setup we use a collection angle of θ > 90° which means that we are recording the backscattering spectrum. Due to the fact that the Fourier transform transforms the sample structural information into an angular dependency of the light field, the method is called angular scattering spectroscopy.

Angular scattering spectroscopy

When a particle is illuminated with a plane wave, the intensity of the (back)scattered light is typically an oscillating function of the angle between the scattered and incident light.

Figure 2 explains how the angular scattering spectrum can be measured. Starting with a simplified case of a one-dimensional recording device, the spectrum is just the intensity at any point on the Fourier plane. The more light of a certain angle is collected by the Fourier lens, the higher the recorded intensity will be at the corresponding point. It doesn't matter where the particle is located, only the angle of the light is important.

With a bit of imagination, one can understand that, for a two-dimensional recording plane (CCD array), there are circles of equal angles. It is possible to calculate the spectrum by summing up intensities on circles centered around the optical axis.

The angular scattering spectrum of spherical particles is like a fingerprint; it is possible to identify the particle sizes by looking at their scattering spectrum and comparing it to spectra generated by a theoretical function (Mie theory) - its characteristics strongly depend on the scatterer size.


Figure 2: Fourier optics (lens)
Incident light from the image plane (left) at a particular angle will be focused at one spot in the Fourier plane (right), regardless of its origin.

References

  1. S. A. Alexandrov, T. R. Hillman, D. D. Sampson, Spatially resolved Fourier holographic light scattering angular spectroscopy, Opt. Lett., vol. 30, no. 24, pp. 3305-3307, 2005.