Coma Aberration

3 Key excerpts on "Coma Aberration"

• 

  eBook - ePub

  Fundamentals of Light Microscopy and Electronic Imaging

  • Douglas B. Murphy, Michael W. Davidson(Authors)
  • 2012(Publication Date)
  • Wiley-Blackwell

    (Publisher)

  Spherical aberration is the undesirable consequence of having lenses figured with spherical surfaces, the only practical approach for lens manufacture. Parallel rays incident at central and peripheral locations on the lens are focused at different axial locations, so that there is not a well-defined image plane, and a point source of light at best focus appears as a spot surrounded by a bright halo or series of rings. For an extended object, the entire image is blurred, especially at the periphery. One common solution is to use a combination of positive and negative lenses of different thicknesses in a compound lens design. Corrections for spherical aberration are made assuming a certain set of conditions: coverslip thickness, the assumption that the focal plane is at or near the coverslip surface, the refractive index of the medium between lens and coverslip, the wavelength of illumination, temperature, and others. Thus, users employing well-corrected objectives can unknowingly induce spherical aberration by using coverslips having the wrong thickness, by warming the objective, or by focusing on objects positioned away from the coverslip surface. Special objectives are now available with adjustable correction collars to minimize spherical aberration (Brenner, 1994).

  Coma is an “off-axis aberration” that causes point objects to look like comets, focused spots with emanating comet tails, located at the periphery of an image. Coma affects the images of points located off the optical axis—that is, when object rays hit the lens obliquely. It is the most prominent off-axis aberration. Rays passing through the edge of the lens are focused farther away from the optical axis than are rays that pass through the center of the lens, causing a point object to look like a comet with the tail extending toward the periphery of the field. Coma is greater for lenses with wider apertures. Correction for this aberration is made to accommodate the diameter of the object field for a given objective.

  Astigmatism

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Fundamental Principles of Optical Lithography

  The Science of Microfabrication

  • Chris Mack(Author)
  • 2011(Publication Date)
  • Wiley

    (Publisher)

  Figure 3.12 .

  3.1.6 Chromatic Aberrations An assumption of the Zernike description of aberrations is that the light being used is monochromatic. The phase error of light transmitted through a lens applies to a specific

  Figure 3.9

  The effect of coma on the pattern placement error of a pattern of equal lines and spaces (relative to the magnitude of the 3rd order x-coma Zernike coefficient Z6 ) is reduced by the averaging effect of partial coherence

  Figure 3.10

  The impact of coma on the difference in linewidth between the rightmost and leftmost lines of a five bar pattern (simulated for i-line, NA = 0.6, sigma = 0.5). Note that the y-oriented lines used here are most affected by x-coma. Feature sizes (350, 400 and 450 nm) are expressed as

  k1 = linewidth *NA/λ

  Figure 3.11 Variation of the resist profile shape through focus in the presence of coma

  Figure 3.12 Examples of isophotes (contours of constant intensity through focus and horizontal position) for (a) no aberrations, and (b) 100mλ of 3rd order coma . (NA = 0.85, λ = 248 nm , σ = 0.5, 150-nm space on a 500-nm pitch)

  wavelength. One expects this phase error, and thus the coefficients of the resulting Zernike polynomial, to vary with the wavelength of the light used. The property of a lens element that allows light to bend is the index of refraction of the lens material. Since the index of refraction of all materials varies with wavelength (a property called dispersion ), lens elements will focus different wavelengths differently. This fundamental problem, called chromatic aberration , can be alleviated by using two different glass materials with different dispersions such that the chromatic aberrations of one lens element cancel the chromatic aberrations of the other. The cemented doublet of Figure 3.2 is the simplest example of a chromatic-corrected lens (called an achromat

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  The Manual of Photography

  • Elizabeth Allen, Sophie Triantaphillidou(Authors)
  • 2012(Publication Date)
  • Routledge

    (Publisher)

  coma patch, from its resemblance to a comet. Coma is significantly reduced by stopping down the lens and can be reduced in a simple lens by placing the aperture stop so that it restricts the area of the lens over which oblique rays are incident. In compound lenses coma is reduced by balancing the error in one element by an equal and opposite error in another. In particular, symmetrical construction is beneficial. Coma is particularly troublesome in wide-aperture lenses.

  Curvature of field

  From the basic lens conjugate equation, the locus of sharp focus for a planar object is the so-called Gaussian plane. In a simple lens, however, this focal surface is in practice not flat but spherical, called the Petzval surface, centred approximately at the rear nodal point of the lens (Chapter 6 ). It is impossible to obtain a sharp image all over the field: when the centre is sharp the corners are blurred, and vice versa. Some large-aperture camera lenses are designed with sufficient residual curvature of field to match the image surface or ‘shell’ of sharp focus to the natural curvature of the film in the gate; a number of slide-projector lenses have been designed in this way. Double-Gauss-derived lenses give a particularly flat image surface, e.g. the Zeiss Planar series of lenses. Given the planar nature of focal plane arrays of imaging elements, it is essential that a lens for digital cameras has a near-flat image surface.

  Astigmatism

  The image surface is the locus of true point images only in the absence of the aberration called astigmatism. This gives two additional curved astigmatic surfaces close to the focal or Petzval surface. The term ‘astigmatic’ comes from a Greek expression meaning ‘not a point’, and the two surfaces are the loci of images of points in the object plane that appear in one case as short lines radial from the optical axis, and in the other as short lines tangential to circles drawn round the optical axis.

  Figure 10.5 a

  shows the geometry of the system, and the occurrence of astigmatism. When light from an off-axis point passes through a lens obliquely, the tangential and radial (sagittal) components are brought to different foci, forming two image ‘shells’ (see Figure 10.5

  Sign up to read

  Learn more about book