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502-20 Chromatic Effects

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502-20 Chromatic Effects 20-1 I and Instrumentation Design Optical OPTI-502 © Copyright 2019 John E. Greivenkamp E. John 2019 © Copyright Section 20 Chromatic Effects 20-2 I and Instrumentation Design Optical OPTI-502 Chromatic Aberration Greivenkamp E. John 2019 © Copyright For a thin lens: 1 nCC1 f 12 Since the index changes with wavelength, so will the focal length. z 1 2 3 Where do Red, Green (or Yellow) and Blue focus? n Because of the higher index for Blue or F light, Blue light is bent more and the Blue focus is closest to the lens. The foci corresponding to the F, d and C wavelengths are not evenly spaced due to the shape of the F d C dispersion curve. 20-3 I and Instrumentation Design Optical OPTI-502 Axial or Longitudinal Chromatic Aberration Greivenkamp E. John 2019 © Copyright Axial chromatic aberration or axial color is a variation of the system focal length with wavelength. FdC z f f = fd FC nCCnCC F 1112 C 12 nnCCFC12 11F C nn ffCF f FC nCCd 1 12 CF CF nd 1 ff f 2 n 1 CF 2 CF d d CF d ddnCC1 12 nnF C dd11f ffCF f 2 d dd FC 20-4 I and Instrumentation Design Optical OPTI-502 Axial Chromatic Aberration - Continued Greivenkamp E. John 2019 © Copyright FCf CF 1 d F cFC FC ddf f f ff f d f 1 CF CF ffCF f Since Abbe numbers are typically 30-70, the longitudinal chromatic aberration of a singlet is 1.5-3% of the focal length. The relative order of the foci is reversed for a negative lens. F focuses closest to the lens for both a positive and a negative lens. Longitudinal focus position: z from d focus Because of the flattening of the dispersion curve, the d-C F d C separation tends to be less than the F-d separation. 20-5 I and Instrumentation Design Optical OPTI-502 Axial Chromatic Aberration of a Negative Lens Greivenkamp E. John 2019 © Copyright For a negative lens, the Blue or F focus remains closest to the lens as Blue light has the largest ray bending. Of course all of the foci are virtual, but the order relative to the lens is the same for a negative or positive lens. F d C d F C z f f = fd The same relationships hold but now the quantities are negative: f 1 f 1 F cFC FC CF ddf f f ffCF f CF ffdd 00 f CFFC f 0 0 20-6 I and Instrumentation Design Optical OPTI-502 Axial or Longitudinal Chromatic Aberration Greivenkamp E. John 2019 © Copyright The blur associated with the chromatic aberration of the objective lens limits the performance of an objective. z Blur To reduce the blur, a small diameter objective lens is required. Since the longitudinal aberration f is constant for a given f, the blur is proportional to the lens diameter. z Blur 20-7 I and Instrumentation Design Optical OPTI-502 Transverse Axial Chromatic Aberration Greivenkamp E. John 2019 © Copyright Transverse axial chromatic aberration measures the image blur size due to axial chromatic aberration. TA rP CH z f f f f The rays from the edge of the pupil are approximately parallel in the vicinity of the focus. Remember that the axial chromatic is 1.5-3% of the focal length and that the diagram is greatly exaggerated. 20-8 I and Instrumentation Design Optical OPTI-502 Transverse Axial Chromatic Aberration Greivenkamp E. John 2019 © Copyright Transverse axial chromatic aberration measures the image blur size due to axial chromatic aberration. Because f f , the three marginal rays (F, d and C) are approximately parallel. Rays from edge of pupil TA TA tanU CH CH f z r U tanU P FdC f f TA r CH P ff TA f 1 TA depends only on the glass and the pupil CH CH radius r (assumes that the stop is at the lens). rfP P r TA P CH 20-9 I and Instrumentation Design Optical OPTI-502 Transverse Axial Chromatic Aberration – Alternate Derrivation Greivenkamp E. John 2019 © Copyright Consider the edge of the lens to be a thin prism of Abbe Number with a deviation and a dispersion . ,0 r P TACH z f rP rP Blur TACH f f f r Blur TAP f CH f The blur is the product of the dispersion and the focal length. rP TACH The ray deviation and dispersion grow as the pupil radius normalized by the focal length. The net result is independent of the focal length. 20-10 I and Instrumentation Design Optical OPTI-502 Lateral Chromatic Aberration Greivenkamp E. John 2019 © Copyright Longitudinal chromatic aberration is chromatic aberration of the marginal ray of the system. Lateral chromatic aberration or lateral color is caused by dispersion of the chief ray. C d F z Stop Image Plane The edge of the lens behaves like a prism. Off-axis image points will exhibit a radial color smear. The blur length increases linearly with image height. Each color has a different lateral magnification. 20-11 I and Instrumentation Design Optical OPTI-502 Achromatic Objective or Doublet Greivenkamp E. John 2019 © Copyright Two lens elements with different dispersive properties are combined into a single objective lens. Red and blue light are made to focus at the same location and a greatly reduced image blur results even with large diameter lenses. z Blur Crown Flint 20-12 I and Instrumentation Design Optical OPTI-502 Achromatic Doublet Greivenkamp E. John 2019 © Copyright The thin lens achromatic doublet corrects longitudinal chromatic aberration by combining a positive thin lens and a negative thin lens. Two different glasses (1, P1 and 2, P2 ) are used. The nominal powers and focal lengths are for d light. 12 12, at d FCFCFC12 For each lens: 1 di i 12 FCi FC ii 12 2 Achromat: FC F C 0 12 11 12 12 ,,12 at d 2 21 22 1 12 2 121 1 1 20-13 I and Instrumentation Design Optical OPTI-502 Secondary Chromatic Aberration Greivenkamp E. John 2019 © Copyright The solution for the thin lens achromatic doublet result forces the same axial focus for F and C light (zero primary chromatic aberration), but d light can focus at a different location. This residual is the secondary chromatic aberration or secondary color of the doublet. dC d C f Cd ff C d nCCnCC11 dC dC12 dC dC11 d 121 C 12 dC11112 nnCC d C dCPP1122 FC FC nndC11 dC11112nnCC F C 12 nn dC PP12 FC11 12 nn 12 dC11 For an achromat: P1 FC11112 nnCC F C 12 nnFC11 PP 1 P 1 dC 12 dC11 FC 1 FC1 1 1 and 11 1 12 1 12 P 2 dC22 FC 2 FC 2 2 PP12 P dC 12 20-14 I and Instrumentation Design Optical OPTI-502 Secondary Chromatic Aberration or Secondary Color Greivenkamp E. John 2019 © Copyright dC f Cd PP21 P dC d C f Cd fff2 C d f 21 dF-C z f = fd fCd Focus shift from d ff d fCd FdC The d focus is probably not the maximum focus shift from F and C. 20-15 I and Instrumentation Design Optical OPTI-502 Partial Dispersion Ratio and the Abbe Number Greivenkamp E. John 2019 © Copyright On a plot of P versus , most glasses lie on a straight line. P nndC PPdC, nnF C n 1 d nnF C P 1 The slope of this line is approximately: 0.00045 2200 Example: BK7 = 64.17 P = .3075 F2 = 36.37 P = .2937 P .0138 1 .0005 27.80 2014 20-16 I and Instrumentation Design Optical OPTI-502 P versus – Real Glass Data Greivenkamp E. John 2019 © Copyright Data for all of the glasses in the Schott Glass Catalog: 0.3200 d,C P 0.3100 0.3000 Partial Dispersion Ratio Partial Dispersion 0.2900 0.2800 0.00 25.00 50.00 75.00 Abbe Number 20-17 I and Instrumentation Design Optical OPTI-502 Singlet versus Doublet Performance Greivenkamp E. John 2019 © Copyright Singlet: fCF 1 f fffCF C F fd 30 70 f Primary chromatic f CF 50 aberration of a singlet. fPCd Doublet: fCdff C d f P 1 0.00045 2200 f Secondary chromatic fCd 2200 aberration of a doublet. The use of the achromatic doublet reduces chromatic focal length variation by a factor of about 40 over the same focal length singlet. 20-18 I and Instrumentation Design Optical OPTI-502 Excess Power Greivenkamp E. John 2019 © Copyright The doublet design places excess power in the positive element that is cancelled by the negative element. Both elements contribute equal, but opposite, amounts of longitudinal chromatic aberration. Just as with the achromatic thin prism, the longitudinal chromatic aberration grows slower with the low dispersion glass (positive element) than the high dispersion glass (negative element). Large differences in the Abbe numbers minimize the excess power and provide better performance. Large Small 20-19 I and Instrumentation Design Optical OPTI-502 Zero Secondary Color Greivenkamp E. John 2019 © Copyright In order to obtain zero secondary chromatic aberration with a doublet, the partial dispersion ratios of the two glasses must be zero. P Pff00 Cd There are some special glass pairs which have different Abbe numbers but the same partial dispersion ratio. Unfortunately, the difference in Abbe number is usually small, resulting in an achromatic doublet with significant excess power. To correct chromatic aberration at additional wavelengths more than two glasses are used: Apochromat – 3 glasses with correction at three wavelengths.
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