Physics
Field Curvature
Field curvature is a phenomenon in which the image formed by a lens is not flat but curved. This occurs because the lens is unable to focus all points in the image plane at the same distance from the lens. As a result, the image appears distorted towards the edges of the field of view.
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5 Key excerpts on "Field Curvature"
eBook - PDFLens Design
A Practical Guide
- Haiyin Sun(Author)
- 2016(Publication Date)
- CRC Press(Publisher)
55 2 Optical Aberrations Any real optical system contains various aberrations. The main task of optical design is to minimize these aberrations. In this chapter, we briefly describe the five important aberrations: spherical aberration, coma, astigmatism, Field Curvature, and image distortion. These five aberrations are monochromatic. We will also describe two chromatic aberrations: longitudinal color and lateral color. 2.1 SPHERICAL ABERRATION 2.1.1 REFLECTION SPHERICAL ABERRATION The most commonly seen aberration is the spherical aberration. Figure 2.1a shows a spherical mirror focusing a ray parallel to its optical axis. The mirror surface has a radius of curvature R, the incident ray has a height of h to the optical axis, and the focused spot is a distance of x away from the center of surface curvature. The incident ray hits one point on the mirror surface and has an angle of θ to the normal of this point on the surface. The reflected ray also has an angle of θ to the normal according to the reflection law. From Figure 2.1a, we have sin( ) θ = h R (2.1) cos( ) θ = R x /2 (2.2) Equation 2.2 holds because the distance between the focused spot and the point where the ray hits the mirror surface also equals to x. Combining Equations 2.1 and 2.2 to solve for the spherical aberration SA = x − R/2, we obtain SA x R R h R = - = - - 2 2 1 1 1 2 0 5 . (2.3) From Equation 2.3, we can see that for a given mirror, the spherical aberration varies as the height of the incident ray varies. When h → 0, SA → 0 and x → R/2. So, R/2 is the paraxial focal length of the mirror. We usually omit the term “par- axial” and simply use the term “focal length.” For h > 0, SA > 0. 56 Lens Design Plotted in Figure 2.1b is a raytracing diagram generated by Zemax showing the spherical aberration of a spherical mirror. Spherical aberration prevents a group of parallel rays being focused at the same spot and is an undesired property.
eBook - PDF- Joseph Braat, Peter Török(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
The curved image surface through F and P can be exploited to compensate for the negative Field Curvature introduced by a subsequent refractive imaging system. It is important to mention that the reasoning above applies to the wavefront aberration due to the intrinsic Petzval Field Curvature of a mirror, in the absence of astigmatism. For a position of the diaphragm at T 0 , on the mirror surface itself, the imaging of a parallel beam suffers also from astigmatism. Inspection of Eqs. (5.3.31)–(5.3.33) shows that, if the diaphragm is at the location of the mirror, identical amounts of astigmatic wavefront aberration and Field Curvature aberration are generated by the spherical mirror. This astigmatism has to be compensated for in the remaining part of the optical system. Fortunately, as for the Field Curvature, the astigmatism introduced by a concave mirror (m T = 0) has the opposite sign to the astigmatism introduced by a (thin) positive lens. • Field Curvature and astigmatism The discussion of Field Curvature so far has not explicitly included astigmatism. In the presence of astigmatism, a flat- field requirement positions the curved tangential and sagittal image surfaces symmetrically with respect to the paraxial image plane. For a single thin lens in air with central stop this symmetric position cannot be obtained. The average tangential and sagittal wavefront aberration is given by W av = 2S 3 + S 4 4 H 2 = −(2n + 1) KH 2 4n , (7.5.6) and the astigmatism enlarges by a factor of (2n + 1) the Field Curvature that follows from the Petzval term S 4 only. An image field that is flat on average can be reached in an extended system where various elements in the system are used with a remote pupil configuration. In this way, in contrast with the single lens with central stop, the curvature of the image field due to astigmatism and the intrinsic Petzval Field Curvature can be uncoupled.
eBook - PDFOptics
Volume 2 of Modern Classical Physics
- Kip S. Thorne, Roger D. Blandford(Authors)
- 2021(Publication Date)
- Princeton University Press(Publisher)
Sometimes the band-width of the light is large, and the variation of the imaging with frequency must be minimized. Sometimes diffractive effects are important. The residual imperfections aberrations of an instrument are known as aberrations. As we have shown, any (geometric-optics) instrument will map, one to many, source points onto detector points. This mapping is usually expanded in terms of a set of basis functions, and several choices are in use, for example, those due to Seidel and Zernike (e.g., Born and Wolf, 1999, Secs. 5.3, 9.2). If we set aside effects caused by chromatic aberration the variation of the refractive index with wavelength, known as chromatic aberration, there are five common types of geometrical aberration. Spherical aberration is the spherical aberration failure to bring a point on the optic axis to a single focus. Instead, an axisymmetric cusp/fold caustic is created. We have already exhibited astigmatism in our discussion of the hyperbolic umbilic catastrophe with a non-axisymmetric lens and an axial source (Sec. 7.5.1). It is not hard to make axisymmetric lenses and mirrors, so this does not happen much in practice. However, as soon as we consider off-axis surfaces, we break the symmetry, and astigmatism is unavoidable. Curvature arises when the curvature surface on which the rays from point sources are best brought to a focus lies on a curved surface, not on a plane. It is sometimes advantageous to accept this aberration and to curve the detector surface. 12 To understand coma, consider a small pencil of coma rays from an off-axis source that passes through the center of an instrument and is brought to a focus. Now consider a cone of rays about this pencil that passes through the periphery of the lens. When there is coma, these rays will on average be displaced 11.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
While distortion can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is barrel distortion, in which the center of the image is magnified more than the perimeter (figure 7a). The reverse, in which the perimeter is magnified more than the center, is known as pincushion distortion (figure 7b). This effect is called lens distortion or image distortion, and there are algorithms to correct it. Systems free of distortion are called orthoscopic (orthos, right, skopein to look) or rectilinear (straight lines). ____________________ WORLD TECHNOLOGIES ____________________ Figure 8 This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g., a focusing screen, intersects the ray passing through the middle of the stop. This assumption is justified if a poor image on the focusing screen remains stationary when the aperture is diminished; in practice, this generally occurs. This ray, named by Abbe a principal ray (not to be confused with the principal rays of the Gaussian theory), passes through the center of the entrance pupil before the first refraction, and the center of the exit pupil after the last refraction. From this it follows that correctness of drawing depends solely upon the principal rays; and is independent of the sharpness or curvature of the image field. Referring to fig. 8, we have O'Q'/OQ = a' tan w'/a tan w = 1/N, where N is the scale or magnification of the image. For N to be constant for all values of w, a' tan w'/a tan w must also be constant.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
in photography. In most cases the surface is concave towards the system. ________________________ WORLD TECHNOLOGIES ________________________ Distortion of the image Fig. 7a: Barrel distortion ________________________ WORLD TECHNOLOGIES ________________________ Fig. 7b: Pincushion distortion Even if the image is sharp, it may be distorted compared to ideal pinhole projection. In pinhole projection, the magnification of an object is inversely proportional to its distance to the camera along the optical axis so that a camera pointing directly at a flat surface reproduces that flat surface. Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While distortion can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is barrel distortion, in which the center of the image is magnified more than the perimeter (figure 7a). The reverse, in which the perimeter is magnified more than the center, is known as pincushion distortion (figure 7b). This effect is called lens distortion or image distortion, and there are algorithms to correct it. ________________________ WORLD TECHNOLOGIES ________________________ Systems free of distortion are called orthoscopic (orthos, right, skopein to look) or rectilinear (straight lines). Figure 8 This aberration is quite distinct from that of the sharpness of reproduction; in unsharp, reproduction, the question of distortion arises if only parts of the object can be recognized in the figure. If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e.g., a focusing screen, intersects the ray passing through the middle of the stop.
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