Optical Coatings

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Fundamental Optics Material Properties Optical Specifications Gaussian Beam Optics Optical Coatings Optical Properties The most important optical properties of a material are its internal and external transmittances, surface reflectances, and refractive indices. The formulas that connect these variables in the on-axis case are presented below. TRANSMISSION External transmittance is the single-pass irradiance transmittance of an optical element. Internal transmittance is the single-pass irradiance transmittance in the absence of any surface reflection losses (i.e., transmittance of the material). External transmittance is of paramount importance when selecting optics for an image-forming lens system because external transmittance neglects multiple reflections between lens surfaces. Transmittance measured with an integrating sphere will be slightly higher. Let T e denote the desired external irradiance transmittance (see equation 4.1), T i the corresponding internal transmittance, t 1 the single-pass transmittance of the first surface, and t 2 the single-pass transmittance of the second surface: 4mt T e = t1t2T i = t1t2e c where e is the base of the natural system of logarithms, m is the absorption coefficient of the lens material, and t c is the lens center thickness. This allows for the possibility that the lens surfaces might have unequal transmittances (for example, one is coated and the other is not). Assuming that both surfaces are uncoated, t t = 14 2r + r 1 2 where ⎛ r = n 4 1 ⎞ ⎜ ⎝ n + 1 ⎟ ⎠ 2 2 is the single-surface single-pass irradiance reflectance at normal incidence as given by the Fresnel formula. The refractive index n must be known or calculated from the material dispersion formula (equation 4.6). These results are monochromatic. Both m and n are functions of wavelength. To calculate either T i or the T e for a lens at any wavelength of interest, first find the value of absorption coefficient m (equation 4.4). Typically, internal transmittance T i is tabulated as a function of wavelength for two distinct thicknesses T c1 and T c2 , and m must be found from these. Thus 1 ⎡1n T i (t c1) 1n T i (t c2) ⎤ m = 4 ⎢ + ⎥ 2 ⎣⎢ t c1 t c2 ⎦⎥ where the bar denotes averaging. In portions of the spectrum where absorption is strong, a value for T i is typically given only for the lesser thickness. Then 1 m = 4 1n T i . t c (4.1) (4.2) (4.3) (4.4) (4.5) When it is necessary to find transmittance at wavelengths other than those for which T i is tabulated, use linear interpolation. The on-axis T e value is normally the most useful, but some applications require that transmittance be known along other ray paths, or that it be averaged over the entire lens surface. The method outlined above is easily extended to encompass such cases. Values of t 1 and t 2 must be found from complete Fresnel formulas for arbitrary angles of incidence. The angles of incidence will be different at the two surfaces; therefore, t 1 and t 2 will generally be unequal. Distance t c , which becomes the surface-to-surface distance along a particular ray, must be determined by ray tracing. It is necessary to account separately for the s- and p-planes of polarization, and it is usually sufficient to average results for both planes at the end of the calculation. REFRACTIVE INDEX AND DISPERSION The Schott Optical Glass catalog offers nearly 300 different optical glasses. For lens designers, the most important difference among these glasses is the index of refraction and dispersion (rate of change of index with wavelength). Typically, an optical glass is specified by its index of refraction at a wavelength in the middle of the visible spectrum, usually 587.56 nm (the helium d-line), and by the Abbé v-value, defined to be v d = (n d 41)/ (n F 4n C ). The designations F and C stand for 486.1 nm and 656.3 nm, respectively. Here, v d shows how the index of refraction varies with wavelength. The smaller v d is, the faster the rate of change is. Glasses are roughly divided into two categories: crowns and flints. Crown glasses are those with n d < 1.60 and v d > 55, or n d > 1.60 and v d > 50. The others are flint glasses. The refractive index of glass from 365 to 2300 nm can be calculated by using the following formula: n = ⎛ 2 2 2 B1l C + B2l C + B3l C + 1 ⎞ ⎜ 2 2 2 ⎟ ⎝ l 4 1 l 4 2 l 4 3 ⎠ Here l, the wavelength, must be in micrometers, and the constants B 1 through C 3 are given by the glass manufacturer. Our tabulation of these constants for the glasses used in our catalog components are presented on page 4.8. Values for other glasses can be obtained from the manufacturer’s literature. This equation yields an index value that is accurate to better than 1!10 45 over the entire transmission range, and even less in the visible spectrum. OTHER OPTICAL CHARACTERISTICS Homogeneity within Melt Homogeneity within melt is the amount of refractive index variation within the manufactured glass blank. Inhomogeneity of refractive index can result in transmitted wavefront distortion. The 1/2 (4.6) 4.4 1 Visit Us OnLine! www.mellesgriot.com
maximum value for homogeneity within melt for all Schott optical glasses used in Melles Griot catalog components is 1!10 44 . Striae Grade Striae are thread-like inclusions within an optical glass. Striae grades are specified in U.S. military specification MIL-G 174B. All Melles Griot catalog components that utilize Schott optical glass are specified to have striae that conform to MIL-G 174B grade A. Grade A means that no visible striae, streaks, or cords are present in the glass. Stress Birefringence Mechanical stress in optical glass leads to birefringence (anisotropy in index of refraction) which can impair the optical performance of a finished component. Optical glass is annealed (heated and cooled) to remove any residual stress left over from the original manufacturing process. Schott Glass defines fine annealed glass to have a maximum of 12 nm/cm of residual stress birefringence for blanks of up to 800 mm in diameter and 100 mm in thickness. APPLICATION NOTE Fused-Silica Optics Synthetic fused silica, described on page 4.11, is an ideal optical material for many laser applications. It is transparent from as low as 180 nm to over 2.0 mm, has low coefficient of thermal expansion, and is resistant to scratching and thermal shock. For more information on some of the specific components manufactured from fused silica, see the following pages: Lenses, pages 6.22–6.29; Mirrors, 9.12–9.17; Beamsplitters, 11.4–11.8. Fundamental Optics Gaussian Beam Optics Optical Specifications Material Properties Optical Coatings Visit Us Online! www.mellesgriot.com 1 4.5
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 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
Page 59: Introduction Glass manufacturers pr
Page 63 and 64: Melles Griot Lens Materials Melles
Page 65 and 66: Refractive Index of Five Schott Gla
Page 67 and 68: Synthetic Fused Silica Fused silica
Page 69 and 70: PERCENT INTERNAL TRANSMITTANCE 99.9
Page 71 and 72: Low-Expansion Borosilicate Glass Th
Page 73 and 74: ZERODUR ® Many optical application
Page 75 and 76: Optical Coatings 5 Optical Coatings
Page 77 and 78: OEM and Special Coatings Melles Gri
Page 79 and 80: PERCENT REFLECTANCE 100 90 80 70 60
Page 81 and 82: will depend on the ratio of optical
Page 83 and 84: v = angle of incidence PERCENT REFL
Page 85 and 86: PERCENT REFLECTANCE PER SURFACE 2.0
Page 87 and 88: Two-Layer Coatings of Arbitrary Thi
Page 89 and 90: ION-ASSISTED BOMBARDMENT Ion-assist
Page 91 and 92: Single-Layer MgF 2 Antireflection C
Page 93 and 94: PERCENT REFLECTANCE 5 4 3 2 1 norma
Page 95 and 96: EXTENDED-RANGE HEBBAR ANTIREFLECTIO
Page 97 and 98: V-Coatings V-coatings are multilaye
Page 99 and 100: Metallic High-Reflection Coatings W
Page 101 and 102: INTERNAL SILVER (/036) $ For intern
Page 103 and 104: Dielectric High-Reflection Coatings
Page 105 and 106: PERCENT REFLECTANCE 100 80 60 40 20
Page 107 and 108: MAXBRIte Coatings MAXBRIte (multi
Page 109 and 110: Laser-Line MAX-R Coatings These mu
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Ultrafast Coating Melles Griot has
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