Imaging Spectroscopy

Background

Experimental spectroscopic techniques are used to acquire information about a target by measuring relative variations in the electromagnetic spectrum. The practice of spectroscopy is very old; its origins are usually attributed to Isaac Newton's separation of white sunlight into a continuum of colors using a glass prism in 1666[1]. Spectroscopy, especially in the visible region, is used by nearly every branch of the physical sciences.

The advent of two dimensional array detectors, specifically the Charge Coupled Device (CCD), permits both spectral and spatial information of an object to be measured simultaneously. This allows for more sophisticated yet still elegant optical systems than previously achieved with point-like detectors such as photomultipliers. Imaging spectroscopy is the practice of such simultaneous spatial-spectral (or hyper spectral) measurements.

The AirSpex Project makes use of a multi-purpose spectral imager, designed by Fred Sigernes at UNIS[2]. Although it can be used in several applications, in this case it is used for daytime, airborne remote sensing of the Earth. The aim of this application of the multi purpose spectral imager is to produce two dimensional images of a distant scene at as many different visible wavelengths as possible with an acceptable spatial and spectral resolution. This three dimensional data volume can then be used in image classification, which is a powerful tool in remote sensing. The details of how similar physical features in a scene can be determined by their spectral response is shown in the analysis section.

Basic spectrographic principles

By using a diffractive element such as a grating or prism (or their combination) one can obtain an intensity distribution of a target as a function of wavelength along one dimension normal to the optical axis. Inclusion of an entrance slit and relay and image-forming optics enable spectra to be acquired in addition to spatial information of the target along the direction of the slit. Figure 1 shows the general principle of imaging spectroscopy in this application. Note that in this figure a combination grating-prism, known as a grism, is the diffractive element.


Figure 1. Application of a spectral imager in airborne remote sensing. Spectral information is
obtained as a function of wavelength across the CCD detector in the x direction, while spatial
information at each scan step is recorded along the slit direction y.

Spatial information in the direction normal to both the slit and the optical axis is obtained by the motion of the imager relative to the scene. This can be achieved by either scanning the imager (e.g. using a scanning mirror or rotating the imager itself), or in the case of AirSpex, moving the imager across the scene from an aircraft. The practicalities of acquiring data in this third dimension of the data volume are described in the instrumentation and flight sections.

A mathematical expression describing the propagation of incident light through the optical system as a function of wavelength is easily calculated for the grism, since the diffraction of the grating and the refractive effect of the prism can be treated separately. A linear-ruled grating diffracts light according to the grating equation:

where k is the integer diffraction order, m is the groove density, &lambda is the wavelength, and &alpha and &beta are the angles before and after diffraction, respectively. Owing to the inclusion of a prism in our case, this equation needs to be modified to account for the wavelength-dependent refraction in the prism. This modified grating equation is

where n is the index of refraction of the prism. The geometry corresponding to this equation is shown in Figure 2.


Figure 2. Grism geometry. G is the location of the
plane grating, and P is the prism of refractive index n.

One advantage in using a grism is that the prism and the grating, while both contributing to the overall dispersion, diffract visible light in opposite senses. Generally speaking, the prism diffracts blue light more strongly than red, while the grating does the opposite. This combination enables the construction of a "straight-through" system where &alpha = -&beta for a chosen center wavelength. A straight-through system is desirable since it preserves the symmetry of the instrument along the optical axis, which minimizes higher order aberrations and other off-axis effects. For one of the spectral imagers used in AirSpex, the straight-through wavelength is found to be 480nm. More details regarding airborne hyperspectral imaging can be found here.


References

1. http://web.mit.edu/spectroscopy/history/history-classical.html
2. Sigernes, F., Lorentzen, D. A., Heia, K. and Svenĝe, T., A multi-purpose spectral imager. Applied Optics, 39, No. 18, 3143-3153 (2000).
3. Airborne Hyperspectral Imaging, F. Sigernes, 2005.


(Finished -JMH 04.05.2005)