Geometric Optics

Typical optics texts begin with a discussion of Fermat’s principle and the concept of wavefronts from which the concept of rays and ray bundles are generated. Following the introduction of the refractive index, we are led to the idea of refraction at an interface between two media. The cornea – air interface can be considered as the model for this; from this, it is possible to deal with total internal reflection. The eye example to use herein is the idea of the viewing of the “angle” which is used in a technique called gonioscopy. One can also use the fact that the photoreceptor captures the incident light and channels them to the site of absorption using the idea of total internal reflection. The crystalline lens is a gradient index medium, and it is possible to teach ray tracing through such media. The iris of the eye, which acts as an aperture, is a good example of both the entrance and exit pupils (image when viewed through the cornea and image when viewed from the retina, after being refracted by the crystalline lens). Curved surface refraction can be thought of as refraction at the various elements (surfaces of the cornea, surfaces of the crystalline lens). Additionally, instead of treating the eye as a thin lens system, we can treat it as a thick lens system and introduce Gaussian points, etc. Another reason to use the eye as a model system is the fact that we can introduce concepts of non-spherical systems (i.e., aspherics) and deal with astigmatic lenses – this concept is rarely taught in traditional optics courses. Because the eye is a decentered system, we can discuss concepts such as prismatic deviation introduced due to a light ray incident at some distance from the optical center (e.g., Prentice’s law). Spherical mirrors can be very easily illustrated by the example of Purkinje – Sanson images (light reflections seen due to reflections at various structures of the eye, namely the anterior corneal surface, posterior corneal surface, anterior lens surface and posterior lens surface). Here, the ideas of Fresnel losses can be introduced. In a more advanced course, it is possible to construct computational eye models and illustrate imaging characteristics by changing the parameters of the model. It is easy (and much welcomed by students) to use the ABCD matrix formalism⁷ in these exercises.

Physical Optics

Physical Optics ideas can be taught by using a number of different examples from the visual system. Interference and the Young double slit experiment has an immediate application in the eye – namely to measure what is known as the grating acuity⁸. This is done by projecting two small coherent spots in the entrance pupil of the eye. These spots will now act as the double slit and produce sine-wave gratings on the retina. As in the traditional Young double slit, by varying the separation between the two spots, we can change the spatial frequency of the fringes and find the limit of vision. This can also lead to finding the contrast threshold for different spatial frequencies. As in the traditional interference experiment, here too, we can define the Michelson contrast, etc. This is just one example. From this, we can generalize and define the modulation transfer function (MTF) and the Optical Transfer function (OTF) and hence, study Fourier optics. Diffraction can be taught by studying imaging by different apertures - more specifically by circular apertures and showing how visual acuity varies depending upon the size of the aperture. When we talk about visual acuity, we are dealing with resolution ability and hence the Rayleigh criterion. Of course, other criteria could be used.

Polarization phenomena can be illustrated by using for example, demonstrations of Haidinger’s brushes. This entoptic phenomenon is due to the polarization properties of short wavelength sensitive photoreceptors in the retina⁹. Light scattering can be illustrated by the presence of floaters in the eye media and the presence of glare. As noted earlier, photoreceptors in the retina behave as classic fiberoptic properties and demonstrate waveguide modes.¹⁰

Wavefront aberrations can be measured using, for example, Hartmann Shack sensors, and this is a major area of research in vision science¹¹. We can describe adaptive optics techniques and descriptions of wavefront aberrations using Zernike polynomials (as well as comparison with Seidel aberrations) using the aberration measurements of the human eye.

Quantum Optics

Photon statistics can be illustrated by analyzing the fact that a dark adapted human eye, under some conditions, needs only about 4-7 photons to give a response of “I see a spot of light” about 60% of the time. In fact, one only needs the absorption of one photon by one photoreceptor to generate a neural response¹². There is also the presence of dark noise. More recently, it has been proposed that human vision can be used to observe entanglement¹³.