Aberrations
Aberrations in physics refer to deviations or distortions in the behavior of waves or particles, leading to errors or imperfections in the formation of an image or the transmission of light. These deviations can occur in optical systems, such as lenses or mirrors, and can result in blurring, distortion, or color fringing. Aberrations are important to understand in order to optimize the performance of optical instruments.
4 Key excerpts on "Aberrations"
eBook - ePubFundamental Principles of Optical Lithography
The Science of Microfabrication
- Chris Mack(Author)
- 2011(Publication Date)
- Wiley(Publisher)
...3 Aerial Image Formation – The Details The impact of Aberrations and defocus must now be added to the description of image formation provided in the previous chapter. The unique aspects of imaging while scanning the mask and wafer past the stationary imaging lens will also be included. Next, a discussion of the vector nature of light and the impact of polarization on imaging will be added and immersion lithography will be described. Finally, a preliminary discussion of image quality will conclude this chapter. 3.1 Aberrations According to Webster, an aberration is ‘… a departure from what is right, true or correct’. In optical imaging, ‘right, true or correct’ can be thought of as the ideal, ‘diffraction-limited’ imaging performance of a lens (which was rigorously defined in the previous chapter using Fourier optics). Thus, a lens aberration is any deviation of the real performance of that lens from its ideal performance. As one might imagine, Aberrations are undesirable intrusions of reality into our attempts to achieve imaging perfection. 3.1.1 The Causes of Aberrations In practice, Aberrations come from three sources – Aberrations of design, Aberrations of construction and Aberrations of use. Aberrations of construction are probably the most tangible sources of errors and include incorrect shapes and thickness of the glass elements that make up the lens, inhomogeneous glass used in their construction, improper mounting, spacings or tilts of the various lens elements, or other imperfections in the manufacture of the lens (Figure 3.1). Aberrations of use include all ways in which improper use of the lens degrades its performance: using the wrong wavelength or wavelength spectrum, tilt of the mask or wafer plane, or incorrect environmental conditions (e.g. changes in the refractive index of air due to changes in temperature, humidity or barometric pressure)...
eBook - ePub- Elizabeth Allen, Sophie Triantaphillidou(Authors)
- 2012(Publication Date)
- Routledge(Publisher)
...Chapter | 10 | Camera lenses Sidney Ray All images © Sidney Ray unless indicated. LENS Aberrations Introduction An understanding of residual Aberrations (errors) is useful in describing the types, merits and imaging limitations of camera lenses. An ‘ideal’ lens forms geometrically accurate images but actual lenses, especially simple ones, do not since the refractive index of glass varies with wavelength, lens surfaces are usually spherical in shape and because of the wave nature of light (see Chapter 2). These cause respectively chromatic Aberrations, spherical Aberrations and diffraction effects. The degrading effects usually increase with both aperture and angle of field. There are seven primary chromatic and spherical Aberrations. Two direct errors or axial Aberrations affect all parts of the image field as well as the central zone, known as axial chromatic aberration and spherical aberration. The other five errors affect only rays passing obliquely through the lens and do not affect the central zone. The effects of these oblique errors, or off-axis Aberrations, increase with the distance of an image point from the lens axis. They are called transverse (or lateral) chromatic aberration (often called ‘lateral colour’), coma, curvature of field, astigmatism and (curvilinear) distortion (see also Chapter 6). Their degrading effects appear in that order as the angular field of view increases. Axial and lateral chromatic Aberrations are chromatic effects; spherical aberration, coma, curvature of field, astigmatism and distortion are spherical effects. The latter are also called Seidel Aberrations after L. Seidel, who in 1856 gave a mathematical treatment of their effects. They are also known as third-order Aberrations, from their mathematical formulation...
eBook - ePubHandbook of Laser Technology and Applications
Lasers: Principles and Operations (Volume One)
- Chunlei Guo, Subhash Chandra Singh, Chunlei Guo(Authors)
- 2021(Publication Date)
- CRC Press(Publisher)
...The laws of refraction (and reflection) apply unchanged. Details are discussed in Chapter C4.2.3. 12.2.5 Evaluation of Aberrations and Diffraction Patterns Standard ray-tracing algorithms include the computation of the optical path difference, the difference between the optical path lengths along the ray and a reference (chief-)ray. By taking a large number of ray samples, typically arranged as a grid raster over the entrance pupil, one obtains a model of the actual wavefront in image space. The Aberrations caused by the passage through the individual surfaces will be mapped into that emerging wavefront and will show up as deformations with respect to its ideal (i.e. spherical) shape. There are several ways in which such a computed wavefront can be evaluated. One is to express its shape by means of Zernike polynomials (see Chapter C1.3), another is to compute the pattern of the power density, which will be created by diffraction in some reference plane. The latter involves addition of the (amplitude) contributions from samples, properly distributed and weighted for the type of beam, and the amplitude distribution associated with its wavefront. Diffraction calculations give the most relevant information for practical purposes, in particular, for systems which approach the theoretical diffraction limit. Care has to be taken to ensure that the samples are taken over the full entrance aperture of the optical system and, thus, represent the true extent of the wavefront, which is admitted by the system’s clear optical diameter. In practice, as already mentioned, this must well exceed the beam diameter to avoid undue beam aperturing. In the diffraction image, any beam aperturing will show up as a broadening of the central peak and a shift of power from that central peak to outer rings. The calculation of the true diffraction pattern for a real beam requires full knowledge of the amplitude distribution within the source beam, which is usually known only for low-order modes...
- Douglas B. Murphy, Michael W. Davidson(Authors)
- 2012(Publication Date)
- Wiley-Blackwell(Publisher)
...(a) The electric field of a planar wavefront becomes disturbed by diffraction upon passage through an aperture. The waves appear to grab hold of the aperture and swing around into its geometric shadow. The amplitude profile of a transmitted wavefront is also no longer uniform and remains permanently altered after passage through the aperture (not shown). (b) A substrate containing a layer of a mixture of fine particles (0.2- and 2- µ m diameter) diffracts an incident planar wavefront into scattered beams that diverge at different angles. The angle of spreading (θ) is inversely proportional to the size of the particles, so θ 1 corresponds to light diffracted by the larger particles. The redirected component of diffracted light is easily observed when a tree or person is backlighted by a strong light source under conditions where the background behind the object is still dark; the bright line outlining the silhouette of the object is diffracted light. Of particular interest to us is the image of a point source of light in the microscope, since images are composed of a myriad of overlapping points. As we will see, waves emanating from a point in the object plane become diffracted at the margins of the objective (or at the edges of a circular aperture at the rear focal plane of the lens), causing the image of the point to look like an extended disk or spot. Thus, the image of a point in a microscope is not a point at all, but a diffraction pattern with a central disk of finite diameter. Because of diffraction, an object’s image never perfectly represents the real object, and there is a limit below which an optical system cannot resolve structural details. Diffraction is also observed when a beam of light illuminates a microscope slide covered with fine dust or scratches (Fig. 5.2 b). The spreading of an automobile’s headlight beams on a foggy night is another good example of the phenomenon...
