Circular lens

As an example, consider a planar wavefront from an incoherent source passing through an aberration-free circular lens. When the image is diffraction-limited, an Airy disc pattern is observed (Goodman, 1996). For an aperture of radius 1 / 2n) the pdf for photon arrival is given by... 

It should be noted that these two definitions are oversimplified in reality, the boundary between the Fraunhofer and Fresnel approximations is not so clear-cut, since the Fresnel-number criterion is a rather crude delimiter. Regardless, for conceptual reasons and simplicity, we only will discuss Fraunhofer diffraction here and restrict the principal treatment to the two most commonly encountered (useful) diffraction objects, namely an elongated straight slit (e.g. as encountered in spectrometers) and a circular aperture (pin holes, diaphragms, any circular lens). 

Fraunhofer diffraction at a circidar aperture dictates the fundamental limits of performance for circular lenses. It is important to note that the ultimate focal spot size d of a circular lens, produced from plane-wave (with wavelength X) illumination of the lens, is... 

Radioactivity, thermal lens, refractive index, circular dichroism, Raman... 

Figure 6.5. Diode laser head. The laser diode output passes successively through a three-element collimating lens, cylindrical lens, and anamorphic prism pair to become a fully collimated, circular, anastigmatic beam. Redrawn from Melles Griot product literature.

The MTF curve can be described mathematically in terms of the above variables. As an example, the MTF [(7/( /)l of a lens employing incoherent illumination and a circular exit pupil is given by... 

When solutions of directly acting choUnomimetics are applied to the eye (i.e., conjunctival sac), they cause contraction of the smooth muscle in two important structures, the iris sphincter and the ciliary muscles (Fig. 12.3). Contraction of the iris sphincter decreases the diameter of the pupil (miosis). Contraction of the circular fibers of the ciliary muscle, which encircles the lens, reduces the tension on the suspensory ligaments that normally stretch and flatten the lens, allowing the highly elastic lens to spontaneously round up and focus for near vision (accommodation to near vision). 

Figure 7 shows an aberration-free intensity distribution at the focus of a typical objective lens similar to that used for DLW lithography. Calculations were carried out using a vectorial Debye theory, which accounts for the polarization effects. For the linearly polarized wave it can be seen that the spot is elongated along the polarization vector. To reduce this asymmetry, a X/4-plate can be used to convert the polarization of the incident beam to circular, which can be interpreted as a combination of two mutually perpendicular linearly polarized components. Thus, width of the photomodified line becomes independent of the beam scanning direction in the sample. 

Lens A lens is a means of changing the shape of a beam of light. In flow cytometry, lenses are used to narrow the laser beam to a small profile at the stream. Some lenses produce a beam with a circular cross-sectional shape others produce beams with an elliptical configuration. Lenses are also used in a flow cytometer to collect scattered light and fluorescence and then to transmit them to an appropriate photodetector. 

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