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OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 20-2 20-1 z 3  2  Because of the higher index for the higher index Because of Blue or F , Blue light is bent is closest the Blue focusmore and to the . d corresponding to the F, The foci and C are not evenly the the shape of to spaced due curve.  1  12 1 Section 20 C nCC length, so will length, so the .  f 1 Chromatic Effects    d F n Where do Red, Green (or Yellow) and Blue ? Where Yellow) Red, Green do (or For a : For a with wave changes Since the index Chromatic 20-3 OPTI-502Optical Designand Instrumentation I

Axial or Longitudinal Chromatic Aberration © Copyright 2019 John E. Greivenkamp

Axial chromatic aberration or axial is a variation of the system focal length with . FdC

z f f = fd

FC  nCCnCC F 1112   C  12 

 nnCCFC12 

11F C nn  ffCF f FC    nCCd 1 12 CF CF nd 1   ff f    2 n 1 CF 2 CF d d CF d   ddnCC1  12  nnF  C dd11f  ffCF f     2    d dd FC

20-4 OPTI-502Optical Designand Instrumentation I

Axial Chromatic Aberration - Continued © Copyright 2019 John E. Greivenkamp

 FCf CF 1 d   F cFC   FC   ddf  f  f ff f d f 1 CF CF ffCF     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 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 OPTI-502Optical Designand Instrumentation I

Axial Chromatic Aberration of a Negative Lens © Copyright 2019 John E. Greivenkamp

For a negative lens, the Blue or F focus remains closest to the lens as Blue light has the largest 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 OPTI-502Optical Designand Instrumentation I

Axial or Longitudinal Chromatic Aberration © Copyright 2019 John E. Greivenkamp

The blur associated with the chromatic aberration of the 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 OPTI-502Optical Designand Instrumentation I

Transverse Axial Chromatic Aberration © Copyright 2019 John E. Greivenkamp

Transverse axial chromatic aberration measures the 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 OPTI-502Optical Designand Instrumentation I

Transverse Axial Chromatic Aberration © Copyright 2019 John E. Greivenkamp

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 and the pupil CH  CH radius r (assumes that the stop is at the lens). rfP  P

r TA  P CH  20-9 OPTI-502Optical Designand Instrumentation I

Transverse Axial Chromatic Aberration – Alternate Derrivation © Copyright 2019 John E. Greivenkamp

Consider the edge of the lens to be a thin prism of  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 OPTI-502Optical Designand Instrumentation I

Lateral Chromatic Aberration © Copyright 2019 John E. Greivenkamp

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 . 20-11 OPTI-502Optical Designand Instrumentation I

Achromatic Objective or © Copyright 2019 John E. Greivenkamp

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 .

z

Blur

Crown Flint

20-12 OPTI-502Optical Designand Instrumentation I

Achromatic Doublet © Copyright 2019 John E. Greivenkamp

The thin lens achromatic doublet corrects longitudinal chromatic aberration by combining a positive thin lens and a negative thin lens. Two different (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 OPTI-502Optical Designand Instrumentation I

Secondary Chromatic Aberration © Copyright 2019 John E. Greivenkamp

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   nCCnCC11 dC dC12 dC dC11 d 121  C  12

dC11112 nnCC d C  

dCPP1122 FC FC nndC11    dC11112nnCC 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 OPTI-502Optical Designand Instrumentation I

Secondary Chromatic Aberration or Secondary Color © Copyright 2019 John E. Greivenkamp

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 OPTI-502Optical Designand Instrumentation I

Partial Dispersion Ratio and the Abbe Number © Copyright 2019 John E. Greivenkamp

On a plot of P versus , most glasses lie on a straight line.

P nndC PPdC, 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 OPTI-502Optical Designand Instrumentation I

P versus – Real Glass Data © Copyright 2019 John E. Greivenkamp

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 OPTI-502Optical Designand Instrumentation I

Singlet versus Doublet Performance © Copyright 2019 John E. Greivenkamp

Singlet:  fCF 1  f  fffCF C F  fd   30 70

f Primary chromatic  f  CF 50 aberration of a singlet.

 fPCd  Doublet:  fCdff 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 OPTI-502Optical Designand Instrumentation I

Excess Power © Copyright 2019 John E. Greivenkamp

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 OPTI-502Optical Designand Instrumentation I

Zero Secondary Color © Copyright 2019 John E. Greivenkamp

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.

Super – 4 or more glasses and wavelengths.

20-20 OPTI-502Optical Designand Instrumentation I

Chromatic Aberration Correction © Copyright 2019 John E. Greivenkamp

In the early , it was believed that chromatic aberration was fundamental and could not be corrected.

Even mistakenly held this belief!

In the mid-1700s, the work of Chester Moor Hall and led to the development of the achromatic objective.

John Dollond 1706-1761, English 20-21 OPTI-502Optical Designand Instrumentation I

The Story of the Achromatic Doublet © Copyright 2019 John E. Greivenkamp

The original inventor is Chester Moor Hall, a Barrister in . In 1733, he commissioned two different opticians, Edward Scarlett and James Mann, to each make one of the lens elements.

By chance, both opticians subcontracted the work to the same man, George Bass. Chester Moor Hall then continued to keep his invention secret.

Chester Moor Hall 1703-1771, English

20-22 OPTI-502Optical Designand Instrumentation I

The Story of the Achromatic Doublet © Copyright 2019 John E. Greivenkamp

Around 1750, George Bass told John Dollond about the he had made, or at least the fact that different glasses have different dispersing powers. Dollond then began a series of experiments using different types of glass.

Dollond’s son, Peter, saw the commercial advantages and once they had made test lenses, patented the invention in 1758.

Peter Dollond 1731-1821, English OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 20-24 20-23 = 1.33. n Red fraction, reflection and dispersion from a from dispersion and reflection fraction, Blue light is deviated more light. red Blue light is deviated more than Blue Raindrops have an index of of water, have Raindrops an index of refraction of water, result from the combination of re of combination the from result Rainbows , primary the For twice. dispersed and refracted is ray entering The raindrop. there is single internal Fresnel reflection. Chester Moor Hall twice attempted to challenge the patent. challenge the attempted twice Hall to Chester Moor is the the invention by profit should who that the person the grounds case on lost his He drawer. his desk keeps it locked in who it, one by not public benefits the who one a landmark patent This was law that remains decision in place today. to in late the of in manufacturer 1700s the dominant to become on went Dollond and early 1800s. The name “Dollond” became for a synonym a . Rainbows –Rainbows Rainbow Primary Achromatic Doublet Patent Doublet Achromatic OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 20-26 20-25 Green Red Green Blue Blue Red ° 51 ° 42 r seen outside the rainbow can be the Sun Light from Observer Blue Red In the primary the droplets rainbow, the primary In light the observer directing the red to those that direct are blue above the rotation light. Because the angle of is the secondary of opposite, the are rainbow reversed. primary The 42°, about angle of is at an rainbow is at 51°. rainbow the secondary and a different set of observer uses Each individual their view to raindrops rainbow. Under good viewing conditions, a second dimme conditions, a second viewing Under good is created reflections there two are rainbow inside the secondary when The bow. primary direction drop. The within the of propagation is drop reversed. Observing Rainbows Observing Rainbows –Rainbows Secondary Rainbow OPTI-502 Optical Design and Instrumentation I OPTI-502 Optical Design and Instrumentation I © Copyright 2019 John E. Greivenkamp © Copyright 2019 John E. Greivenkamp 20-28 20-27 dependence. a As 4  Red Sunset green content of the direct the direct content green sunlight, leaving of ng The centers sunlight. the incident for Scattered Blue Sunlight Blue Scattering Up-Looking Sensor Sun Sunsets are red for the same reason that the sky is blue. The long path length through the path length through long The is blue. the same the sky that reason for Sunsets are red atmosphere at sunset depletes and the blue oranges. and reds Molecules in the atmosphere act as scatteri 1/ a has which scattering Rayleigh is mechanism scattering primary result, blue light is preferentially result, light is preferentially blue scattered, blue. appears the sky and Why are Sunsets Red? are Sunsets Why Why is the Sky Blue? Sky is the Why