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Fundamental Optics Material Properties Optical Specifications Gaussian Beam Optics COMA In spherical lenses, different parts of the lens surface exhibit different degrees of magnification. This gives rise to an aberration known as coma. As shown in figure 1.17, each concentric zone of a lens forms a ring-shaped image called a comatic circle. This causes blurring in the image plane (surface) of off-axis object points. An off-axis object point is not a sharp image point, but it appears as a characteristic comet-like flare. Even if spherical aberration is corrected and the lens brings all rays to a sharp focus on axis, a lens may still exhibit coma off axis. See figure 1.18. As with spherical aberration, correction can be achieved by using multiple surfaces. Alternatively, a sharper image may be produced by judiciously placing an aperture, or stop, in an optical system to eliminate the more marginal rays. FIELD CURVATURE Even in the absence of astigmatism, there is a tendency of optical systems to image better on curved surfaces than on flat planes. This effect is called field curvature (see figure 1.19). In the presence of astigmatism, this problem is compounded because there are two separate astigmatic focal surfaces that correspond to the tangential and sagittal conjugates. Field curvature varies with the square of field angle or the square of image height. Therefore, by reducing the field angle by one-half, it is possible to reduce the blur from field curvature to a value of 0.25 of its original size. S 1′ 1 1 1′ 1 1′ P,O Figure 1.18 Figure 1.19 points on lens 1 4 2 1′ 4′ 2′ 3 3′ 0 3′ 3 2′ 4′ 1′ 2 4 1 positive transverse coma focal plane Positive transverse coma spherical focal surface Field curvature corresponding points on S 1 4 1′ 2 4′ 2′ 3 3′ S 60° Optical Coatings Figure 1.17 Imaging an off-axis point source by a lens with positive transverse coma 1.14 1 Visit Us OnLine! www.mellesgriot.com
Positive lens elements usually have inward curving fields, and negative lenses have outward curving fields. Field curvature can thus be corrected to some extent by combining positive and negative lens elements. DISTORTION The image field not only may have curvature but may also be distorted. The image of an off-axis point may be formed at a location on this surface other than that predicted by the simple paraxial equations. This distortion is different from coma (where rays from an off-axis point fail to meet perfectly in the image plane). Distortion means that even if a perfect off-axis point image is formed, its location on the image plane is not correct. Furthermore, the amount of distortion usually increases with increasing image height. The effect of this can be seen as two different kinds of distortion: pincushion and barrel (see figure 1.20). Distortion does not lower system resolution; it simply means that the image shape does not correspond exactly to the shape of the object. Distortion is a separation of the actual image point from the paraxially predicted location on the image plane and can be expressed either as an absolute value or as a percentage of the paraxial image height. It should be apparent that a lens or lens system has opposite types of distortion depending on whether it is used forward or backward. This means that if a lens were used to make a photograph, and then used in reverse to project it, there would be no distortion in the final screen image. Also, perfectly symmetrical optical systems at 1:1 magnification have no distortion or coma. CHROMATIC ABERRATION The aberrations previously described are purely a function of the shape of the lens surfaces, and can be observed with monochromatic light. There are, however, other aberrations that arise when these optics are used to transform light containing multiple wavelengths. OBJECT PINCUSHION DISTORTION BARREL DISTORTION The index of refraction of a material is a function of wavelength. Known as dispersion, this is discussed in Chapter 4, Material Properties. From Snell’s law (see equation 1.20), it can be seen that light rays of different wavelengths or colors will be refracted at different angles since the index is not a constant. Figure 1.21 shows the result when polychromatic collimated light is incident on a positive lens element. Because the index of refraction is higher for shorter wavelengths, these are focused closer to the lens than the longer wavelengths. Longitudinal chromatic aberration is defined as the axial distance from the nearest to the farthest focal point. As in the case of spherical aberration, positive and negative elements have opposite signs of chromatic aberration. Once again, by combining elements of nearly opposite aberration to form a doublet, chromatic aberration can be partially corrected. It is necessary to use two glasses with different dispersion characteristics, so that the weaker negative element can balance the aberration of the stronger, positive element. Variations of Aberrations with Aperture, Field Angle, and Image Height Aberration Lateral Spherical Longitudinal Spherical Coma Astigmatism Field Curvature Distortion Chromatic white light ray Aperture blue light ray blue focal point red light ray red focal point Figure 1.20 Pincushion and barrel distortion Figure 1.21 Longitudinal chromatic aberration (Ω) Ω 3 Ω 2 Ω 2 Ω Ω — — Field Angle (ß) — — ß ß 2 ß 2 ß 3 — Image Height (y) — — y y 2 y 2 y 3 — longitudinal chromatic aberration Fundamental Optics Gaussian Beam Optics Optical Specifications Material Properties Optical Coatings Visit Us Online! www.mellesgriot.com 1 1.15
Page 1 and 2: Fundamental Optics 1 Introduction 1
Page 3 and 4: Paraxial Formulas SIGN CONVENTIONS
Page 5 and 6: object F 2 Figure 1.4 image Example
Page 7 and 8: Figure 1.6 Figure 1.7 f f 2 object
Page 9 and 10: Figure 1.8 Figure 1.9 INDIVIDUAL EL
Page 11 and 12: Performance Factors After paraxial
Page 13: third-order, monochromatic, spheric
Page 17 and 18: Lens Shape Aberrations described in
Page 19 and 20: ay f-numbers 2.7 3.3 4.4 6.7 13.3 S
Page 21 and 22: AIRY DISC DIAMETER = 2.44 l f/# Fig
Page 23 and 24: Lens Selection Having discussed the
Page 25 and 26: Example 4: Diffraction-Limited Perf
Page 27 and 28: Aberration Balancing To improve sys
Page 29 and 30: Definition of Terms FOCAL LENGTH (f
Page 31 and 32: infinity (which is a comfortable vi
Page 33 and 34: For symmetric lenses (r 2 = 4r 1 ),
Page 35 and 36: Separation of Nodal Point from Corr
Page 37 and 38: Gaussian Beam Optics 2 Introduction
Page 39 and 40: Even if a Gaussian TEM 00 laser-bea
Page 41 and 42: eam expander INCORPORATING M 2 INTO
Page 43 and 44: M 2 AND THE LENS EQUATION For real-
Page 45 and 46: employed when laser power must be c
Page 47 and 48: Figure 2.13 Keplerian beam expander
Page 49 and 50: Optical Specifications 3 Wavefront
Page 51 and 52: Centration The mechanical axis and
Page 53 and 54: PERFECT RECTANGULAR LENS The MDMTF
Page 55 and 56: The permissible number of maximum-s
Page 57 and 58: Material Properties 4 Material Prop
Page 59 and 60: Introduction Glass manufacturers pr
Page 61 and 62: maximum value for homogeneity withi
Page 63 and 64: Melles Griot Lens Materials Melles
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Refractive Index of Five Schott Gla
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Synthetic Fused Silica Fused silica
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PERCENT INTERNAL TRANSMITTANCE 99.9
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Low-Expansion Borosilicate Glass Th
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ZERODUR ® Many optical application
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Optical Coatings 5 Optical Coatings
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OEM and Special Coatings Melles Gri
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PERCENT REFLECTANCE 100 90 80 70 60
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will depend on the ratio of optical
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v = angle of incidence PERCENT REFL
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PERCENT REFLECTANCE PER SURFACE 2.0
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Two-Layer Coatings of Arbitrary Thi
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ION-ASSISTED BOMBARDMENT Ion-assist
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Single-Layer MgF 2 Antireflection C
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PERCENT REFLECTANCE 5 4 3 2 1 norma
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EXTENDED-RANGE HEBBAR ANTIREFLECTIO
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V-Coatings V-coatings are multilaye
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Metallic High-Reflection Coatings W
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INTERNAL SILVER (/036) $ For intern
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Dielectric High-Reflection Coatings
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PERCENT REFLECTANCE 100 80 60 40 20
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MAXBRIte Coatings MAXBRIte (multi
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Laser-Line MAX-R Coatings These mu
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Ultrafast Coating Melles Griot has
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