Page 134 - Vibrational Spectroscopic Imaging for Biomedical Applications

110 Cha pte r F o u r

sample is defined by the size of the remote aperture, in the case of
a single element detector, or the pixel size in the case of a linear
array. For example, in the Perkin Elmer Spotlight 300 the pixel size on
the array is 30 × 30 μm, which results in a pixel resolution at the sample
of 1.6 × 1.6 μm. The total area that can be imaged is dependent upon
the size of the hemisphere and is limited by spherical aberrations
associated with large off-axis positions. For a 3-mm diameter hemi-
sphere, the sample area is on the order of 100 × 100 μm and that for a
25-mm diameter hemisphere is on the order of 2500 × 2500 μm.
Whether on-axis or off-axis imaging is employed, the incidence angle
changes slightly for each sample position. As a result, the penetration
depth (optical path length) is different for different sample locations. 26
However, this change in penetration depth can normalized much like
a macro-ATR spectrum is normalized for penetration depth as a func-
tion of wavelength.
In the previous discussion of ATR imaging, the pixel resolution
was quoted for each method. Pixel resolution gives no indication of
the spatial resolution inherent with the method. In the introduction to
this chapter, Eq. (4.1) gives the diffraction limited diameter of a beam
of light focused to a point with a lens or objective. The radial intensity
distribution of the focused beam from the optic axis has the form of a
Bessel function given by: 8,37

(
(
IP () = 1 ⎡ ⎢ ⎛2 J kaw)⎞ − ε 2 ⎛ 2 J kaw)⎞⎤ ⎥ 2 I (4.6)
1
1
( −1 ε 22 ⎣ ⎜ kaw ⎟ ⎠ ⎜ ⎝ kaw ⎟ ⎠ ⎥ ⎦ 0
w
) ⎝ ⎢
The distribution is also known as the Airy pattern or point spread
function (PSF) for an optical system. A plot of the distribution for the
annular aperture present in a reflecting objective is given in Fig. 4.5.
Values employed to obtain the distribution include sin θ = 0.3, n = 4.0,
λ = 6.0 and an obscuration value of 0.31. The distribution shows that
the distance between the first minima from the origin is approxi-
mately 6 μm, which is d given by Eq. (4.1). Contained within this
diameter is 84 percent of the original energy from the source, with the
remaining 16 percent distributed over larger diameters.
By integrating the PSF one obtains the step function also shown
in the plot. To evaluate the spatial resolution of a microscope, one
usually translates the edge of a polymer film through the focus of
the microscope and monitors the intensity of an absorption as a
function of position. After normalization of the intensity values,
the distance between those abscissa values with associated inten-
sity values 0.08 and 0.92 (8 and 92 percent) is taken as the spatial reso-
lution. For convenience, the 5 and 95 percent or 10 and 90 percent
distance has been reported. Equation (4.1) is employed as the mea-
sure of spatial resolution for infrared microspectroscopy because for
a sample of that size (6 μm) one would expect 16 percent contamination