Optical Coatings

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Fundamental Optics Material Properties Optical Specifications Gaussian Beam Optics Optical Coatings Lens Combination Formulas PARAXIAL LENS COMBINATION FORMULAS Many optical tasks require several lenses in order to achieve an acceptable level of performance. One possible approach to lens combinations is to consider each image formed by each lens as the object for the next lens and so on. This is a valid approach, but it is time consuming and unnecessary. It is much simpler to calculate the effective (combined) focal length and principal-point locations and then use these results in any subsequent paraxial calculations (see figure 1.8). They can even be used in the optical invariant calculations described in the preceding section. EFFECTIVE FOCAL LENGTH The following formulas show how to calculate the effective focal length and principal-point locations for a combination of any two arbitrary components. The approach for more than two lenses is very simple: calculate the values for the first two elements, then perform the same calculation for this combination with the next lens. This is continued until all lenses in the system are accounted for. The expression for the combination focal length is the same whether lens separation distances are large or small and whether f 1 and f 2 are positive or negative: f = 1 f ff 1 2 f 1 + f2 4 . d This may be more familiar in the form s ′′ = 2 = 1 f + 1 f 4 d ff . 1 2 1 2 f 2 (f1 4 d) . f + f 4 d 1 2 z = s 2′′ 4 f . (1.16) (1.17) Notice that the formula is symmetric with respect to interchange of the lenses (end-for-end rotation of the combination) at constant d. The next two formulas are not. COMBINATION FOCAL-POINT LOCATION For all cases, COMBINATION SECONDARY PRINCIPAL-POINT LOCATION (1.18) Because the thin-lens approximation is obviously highly invalid for most combinations, the ability to determine the location of the secondary principal point is vital for accurate determination of d when another element is added. The simplest formula for this calculates how far the secondary principal point of the final (second) element is moved by being part of the combination: (1.19) COMBINATION EXAMPLES It is possible for a lens combination or system to exhibit principal planes that are far removed from the system. When such systems are themselves combined, negative values of d may occur. Probably the simplest example of a negative d-value situation is shown in figure 1.9. Meniscus lenses with steep surfaces have external principal planes. When two of these lenses are brought into contact, a negative value of d can occur. Other combined-lens examples are shown in figures 1.10 through 1.13. SYMBOLS f f 1 f 2 d = combination focal length (EFL), positive if combination final focal point falls to right of combination secondary principal point, negative otherwise. = focal length (EFL) of first element. = focal length (EFL) of second element. = distance from secondary principal point of first element to primary principal point of second element (positive if primary principal point is to right of the secondary principal point, negative otherwise). s 2 ″ = distance from secondary principal point of second element to final combination focal point (location of final image for object at infinity to left), positive if the focal point is to right of second element secondary principal point. z = distance to combination secondary principal point measured from secondary principal point of second element, positive if combination secondary principal point is to right of secondary principal point of second element. Note: These paraxial formulas apply to coaxial combinations of both thick and thin lenses immersed in any fluid with refractive index independent of position. They assume that light propagates from left to right through an optical system. 1.8 1 Visit Us OnLine! www.mellesgriot.com
Figure 1.8 Figure 1.9 INDIVIDUAL ELEMENT 1st element COMBINATION 2 elements SUBSYSTEM d d 2nd element z, from formula 3rd element combination secondary principal plane (to find combination primary principal plane, apply procedure to reversed combination resulting from end-to-end rotation) subsystem secondary principal plane n-1 elements nth element to be added to complete the system d z, from formula system secondary COMPLETE SYSTEM principal plane principal planes not “crossed” system primary principal plane (secondary principal plane located by z formula for reversed system) lens combinations or systems may exhibit “crossed” principal planes; single lenses cannot SUBSYSTEM principal planes internal but “crossed” n-1 elements Generalization from combinations to systems 1 2 3 4 d subsystem secondary principal plane nth element to be added to complete the system subsystem primary principal plane 3 4 1 2 d>0 d
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: Figure 1.6 Figure 1.7 f f 2 object
Page 11 and 12: Performance Factors After paraxial
Page 13 and 14: third-order, monochromatic, spheric
Page 15 and 16: Positive lens elements usually have
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
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Introduction Glass manufacturers pr
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maximum value for homogeneity withi
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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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Optical Coatings

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