OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-1 Section 21 Chromatic Effects OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-2 z 3 2 Because of the higher index for of the higher index Because Blue or F light, Blue light is bent focus is closest the Blue more and to the lens. d to the F, foci corresponding The are not evenly and C wavelengths of the to the shape due spaced dispersion curve. 1 12 1 C nCC f 1
d F n Where do Red, Green (or Yellow) and Blue focus? Yellow) Green (or Where do Red, For a thin lens: so will the focal length. with wavelength, Since the index changes Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 2 21-3
CF d
f FC 2 z
2 dd 11 CF CF CF d dd
11 C CF CF CF ff f ff f ff f
f a variation of the system focal length with Fd 12 d 1 f = f f = nCC 12 12 12 dd 11 1 d 12 d nCC nCCnCC 1 1 d FC n d nn FC FC n FC FC F C nn nnCC
wavelength. Axial chromatic aberration or axial color is Axial or Longitudinal Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-4
1 1
C f f f f
d
FC CF dd F d f d a negative lens. F focuses closest to the lens e longitudinal chromatic aberration of a CF z from FC d focus ff
CF CF Fc FC ff f
f Since Abbe numbers are typically 30-70, th singlet is 1.5-3% of the focal length. relative The order of the foci is reversed for for both a positive and a negative lens. Longitudinal focus position: Because of the flattening Because the d-C dispersion curve, separation tends to be less than the F-d separation. Axial Chromatic Aberration - Continued OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-5 d F C z
1 f f
1 f f s closest to the lens as Blue light has are virtual, but the order relative to the lens FC CF dd 00 0 0 d F dd CFFC f = f f = ff f f
d f CF CF Fc FC ff f C
f The same relationships hold but now the quantities are negative: same relationships hold but now The largest ray bending. Of course all of the foci largest ray bending. is the same for a negative or positive lens. For a negative lens, the Blue or F focus remain Axial Chromatic Aberration of a Negative Lens OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-6 z z Blur Blur lens is required. Since the longitudinal is proportional to the lens diameter. aberration of the objective lens limits the f is constant for a given f, the blur aberration The blur associated with the chromatic The performance of an objective. To reduce the blur, a small diameter objective Axial or Longitudinal Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp z 21-7 f CH TA f
e focus. Remember that the ures the image blur size due to axial ures the image blur size due f f The rays from the edge of the pupil are approximately rays from the edge The parallel in the vicinity of th axial chromatic is 1.5-3% of the focal length and that the axial chromatic is 1.5-3% of the focal length and diagram is greatly exaggerated. P r Transverse Axial Chromatic Aberration chromatic aberration. chromatic aberration. Transverse axial chromatic aberration meas OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-8 z C CH TA f U Fd (assumes that the stop is at the lens). is at the (assumes that the stop P Rays from depends only on the glass and the pupil the glass and only on depends edge of pupil CH radius r TA ures the image blur size due to axial ures the image blur size due
1 f CH
P f f r TA f P
P r r f U U ff CH CH CH P rf TA TA tan tan TA Because , the three Because d and C) are rays (F, marginal approximately parallel. chromatic aberration. chromatic aberration. Transverse axial chromatic aberration meas Transverse Axial Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp z 21-9 and ,0 P f r CH with a deviation TA f P r The blur is the product of the dispersion and the of the dispersion and blur is the product The focal length. as the dispersion grow ray deviation and The pupil radius normalized by the focal length. of the focal length. net result The is independent f be a thin prism Number of Abbe erration – Derrivation Alternate f P r CH CH P r CH lur TAlur f TA f . B B TA P r Transverse Axial Chromatic Ab a dispersion Consider the edge of the lens to the edge Consider OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-10 z d F C aberration of the marginal ray image height. Each color has a different image height. Each color has a different Plane Image f-axis image points will exhibit a radial color is caused by dispersion of the chief ray. by is caused Stop The edge of the lens behaves like a prism. Of of the lens behaves edge The blur length increases linearly with The smear. lateral magnification. system. lateral Lateral chromatic aberration or color Longitudinal chromatic aberration is Lateral Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-11 z Blur e same location and a greatly reduced image a greatly reduced e same location and ve properties are combined into a single into a combined ve properties are Flint Crown objective lens. Red and blue light are made to focus at th with large diameter lenses. blur results even Two lens elements with different dispersi Two Achromatic Objective or Doublet OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-12 ) are 12
2 2 ,, at d ,, at
, P 2 and 1 1 , P 1 12 12 22 11
ii di i ongitudinal chromatic aberration by combining ongitudinal chromatic aberration by
FCi , at d , at
12 For each lens: For each 0 in lens. Two different glasses ( in lens. Two 2 1 FC F C 12
12 12 2 1 FC FC FC 121 1 12 FC 21 12 12 Achromat: used. The nominal powers and focal lengths are for d light. and nominal powers The used. a positive thin lens and a negative th a positive thin lens and The thin lens achromatic doublet corrects l The Achromatic Doublet OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-13 2 2 1 1
2 1 FC FC
nnCC 11112 FC F C axial focus for F and nnCC P P 11 22 2 11 1 11 11 dC FC dC FC dC FC 11 11 nn nn dC FC nnCC nCCnCC and nn nn 11112 11112 11 121 12 1 dC F C dC d C dC d C light can focus at a different location. This P
result forces the same rration or secondary color of the doublet. rration or secondary
ff 12 12 P f 1 1
12 1 12
12 11 1 12 12
12 12 12 PP PP 1122 12 PP PP dC dC d C Cd C d dC FC FC dC dC dC dC dC achromat: For an The solution for the thin lens achromatic doublet The C light (zero primary chromatic aberration), but d chromatic abe residual is the secondary Secondary Chromatic Aberration OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-14 2 z fff f Cd f dF-C dC d C Cd C d
Cd f d f = f f = P FdC d 21 21
PP ff from d Focus shift f f dC Cd The d focus is probably not the maximum focus shift from F and C. Secondary Chromatic Aberration or Secondary Color Chromatic Aberration or Secondary Secondary OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-15 1 dC FC nn nn d FC n nn , dC
1 2200 PP 0.00045
P .0005 = .3075 = .2937 = 64.17 = 36.37
P P .0138 1 27.80 2014
P F2 , most glasses lie on a straight line. , most glasses lie on versus P P Example: BK7 The slope of this line is approximately: slope of The On a plot of Partial Number Dispersion Ratio and the Abbe OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-16
Abbe Number in the Schott Glass Catalog: 0.00 25.00 50.00 75.00 – Glass Data Real
0.3200 0.3100 0.3000 0.2900 0.2800
d,C P Partial Dispersion Ratio Dispersion Partial Data for all of the glasses P versus OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-17
1 CF d f Secondary chromatic aberration of a doublet. f Primary chromatic aberration of a singlet.
P romatic focal length variation by a factor romatic focal length variation by 1 Cd 2200 f f
f f 2200 50 0.00045 30 70 Cd CF f f
P
CF C F fff ff
Cd C d f f The use of the achromatic doublet reduces ch use of the achromatic doublet reduces The of about 40 over the same focal length singlet. Doublet: Singlet: Singlet versus Doublet Performance Doublet Singlet versus OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-18 Small ounts of longitudinal chromatic aberration. t) than the high dispersion glass (negative e positive element that is cancelled by the e positive element that is cancelled by longitudinal chromatic aberration grows slower longitudinal chromatic aberration grows Large negative element. Both elements contribute equal, but opposite, am Just as with the achromatic thin prism, with the low dispersion glass (positive elemen element). better provide and numbers minimize power the excess Large differences in the Abbe performance. The doublet design places excess power in th The doublet design places excess power Excess Power OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-19 wavelengths more than two glasses are used: fference in Abbe number is usually small, fference in Abbe ve different Abbe numbers but the same tic aberration with a doublet, the partial tic aberration with a doublet,
P Cd
00 Pff Apochromat – 3 glasses with correction at three wavelengths. Super Apochromat – 4 or more glasses and wavelengths. dispersion ratios of the two glasses must be zero. glasses must be dispersion ratios of the two ha There are some special glass pairs which partial dispersion ratio. Unfortunately, the di resulting in an achromatic doublet with significant power. excess To correct chromatic aberration at additional In order to obtain zero secondary chroma In order to obtain zero secondary Zero Secondary Color Zero Secondary OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-20 matic aberration was fundamental and could matic aberration was fundamental and John Dollond 1706-1761, English In the mid-1700s, the work of Chester Moor Hall and the work In the mid-1700s, John Dollond led to the development of the achromatic objective. not be corrected. mistakenly held this Even Isaac Newton belief! In the early 1700s, it believed that chro was In the early 1700s, Chromatic Aberration Correction OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-21 to the same man, George Bass. Chester Bass. to the same man, George James Mann, to each make one of the lens a Barrister in London. In 1733, he commissioned a Barrister In 1733, in London. Chester Moor Hall 1703-1771, English two different opticians, Edward Scarlett two different opticians, Edward and elements. By chance, both opticians subcontracted the work his invention secret. to keep Moor Hall then continued The original inventor is Chester Moor Hall, The The Story of the Achromatic Doublet The OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-22 ages and once they had made test lenses, Peter Dollond 1731-1821, English fferent dispersing fferent powers. Dollond then began a ng different types of glass. ng different The Story of the Achromatic Doublet The Around 1750, George Bass told John Dollond about the achromatic lens he had made, or at the achromatic lens he had about Dollond Bass told John George 1750, Around di glasses have least the fact that different series of experiments usi saw the commercial advant son, Peter, Dollond’s patented the invention in 1758. OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-23 on who should profit by the invention is the law that remains in place to today. Dollond went on to become the dominant manufacturer of telescopes in late 1700s to become on went Dollond for a telescope. a synonym became name “Dollond” The early 1800s. and one who benefits the public by it, not one who keeps it locked in his desk drawer. a landmark decision in patent This was Chester Moor Hall twice attempted to challenge the patent. Chester Moor Hall twice attempted to challenge that the pers the grounds lost his case on He Achromatic Doublet Patent OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-24 = 1.33. n Red fraction, reflection and dispersion from a dispersion fraction, reflection and dispersed twice. For the primary rainbow, Blue light is deviated more than red light. Blue Raindrops have an index of refraction of water, an index of refraction Raindrops have of water, raindrop. The entering ray is refracted and raindrop. The there is single internal Fresnel reflection. Rainbows result from the combination of re Rainbows Rainbows – Primary Rainbow OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-25 when there are two reflections inside the when mmer rainbow can be seen outside the Blue Red primary bow. The secondary rainbow is created drop. The direction of propagation within the drop is reversed. Under good viewing conditions, a second di Rainbows – Rainbow Secondary OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-26 Blue Red Green Red Green Blue ° 51 ° 42 the Sun Light from Observer In the primary rainbow, the droplets In the primary rainbow, directing the red light to observer that direct the blue those are above the angle of rotation is light. Because opposite, the colors of secondary rainbow are reversed. The primary rainbow is at an angle of about 42°, and the secondary rainbow is at 51°. Each observer uses a different set of raindrops to view their individual rainbow. Observing Rainbows OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-27 dependence. As a 4 ng centers for the incident sunlight. The Scattered Blue Sunlight Up-Looking Sensor primary scattering mechanism is Rayleigh scattering which has a 1/ has scattering which is Rayleigh primary scattering mechanism Molecules in the atmosphere act as scatteri result, blue light blue. is preferentially the sky appears scattered, and Why is the Sky Blue? OPTI-201/202 Geometrical and Instrumental Optics © Copyright 2018 John E. Greivenkamp 21-28 Red Sunset sky is blue. The long path length through the green content of the direct sunlight, leaving Blue Scattering Sun atmosphere at sunset depletes the blue and oranges. reds and Sunsets are red for the same reason that Why are Sunsets Red? Why