Page 33 - Computational Retinal Image Analysis

2 Optics of the eye 23

blurring during the image formation is described by the point-spread function (PSF).
The PSF serves a similar purpose in describing image formation as the concept of
the ‘impulse response’ in the analysis of signals and systems—in fact the PSF is the
square of the modulus of the two-dimensional spatial impulse response. The PSF of
the ocular media varies significantly across the eye and can be accurately modeled
using optical ray-tracing programs and various schematic eye models [8–10], but
over small areas of the retina, the blurring of the retinal image can be considered as
the convolution of an ideal retinal image with the local eye PSF.
The concept of the ‘ideal retinal image’ requires some comment: whereas opaque
objects such as, optical test targets, do not change appearance substantially with
changes in illumination, light propagates diffusely through the complex structure
of the retina and this imprints a further signature on image quality. Although the
concept of a tissue PSF can help in the appreciation of the reduction of image con-
trast in biomedical imaging [11] the complex heterogeneity of the retina limits the
usefulness of this concept for retinal imaging. Nevertheless retinal images exhibit a
contrast that varies strongly with the size of an approximate tissue PSF, between for
example blue light, where the tissue PSF is typically a few tens of microns and red
or near infrared light where it can be a few millimeters. This is discussed further in
Section 2.5 and highlighted by the images in Fig. 5.
The low-pass filter function for the spatial frequencies in a retinal image is deter-
mined by the modulation-transfer-function (MTF) of the eye, which is determined
both by the physics of diffraction and also by the optical aberrations of the eye.
Additional optical aberrations introduced by the ophthalmoscope can further reduce
resolution, particularly at large field angles or with unintentional defocus. As for any
imaging system, when the pupil is small (corresponding to a large f/#, or a small
numerical aperture, henceforth NA), the wave nature of light means that diffraction
limits the full-width, half-maximum (FWHM) angular resolution to
λ
.
δθ =122 (1)
nD
where λ is the wavelength of light, n is refractive index (about 1.3 for the ocular
media) and D is the diameter of the imaging aperture. The corresponding feature
size that can be imaged at the retina is given simply by d = f × δθ where f is the fo-
cal length of the eye (assumed equal to the internal diameter of the eye ball). If the
resolution of the eye is limited only by diffraction then for green light and a dilated
pupil with D = 8 mm, the limiting angular resolution of 60 μradians would enable
imaging of retinal features as small as 1.4 μm—that is the rods and cones could eas-
ily be resolved. However, the optical aberrations of the eye, like any imaging system,
tend to limit the angular resolution above a certain pupil diameter: for the human eye
the limiting angular resolution corresponds to the diffraction limit of a 2-mm pupil
[13]: that is about 250 μradians enabling features down to a width of about 6 μm to
be imaged. It should be noted however, that the use of adaptive optics can enable
correction of optical aberrations to enable imaging with a resolution close to the dif-
fraction limit, which enables individual photoreceptors to be imaged [14]. It should
further be noted, that the eye, like any imaging system, acts as a low-pass filter of