Section 20. Chromatic Effects

Size: px

Start display at page:

Download "Section 20. Chromatic Effects"

Ada Morris
5 years ago
Views:

1 Section 0 Chromatic Eects 0- Chromatic Aberration For a thin lens: n C C Since the inex changes with wavelength, so will the ocal length Where o Re, Green (or Yellow) an Blue ocus? n F C Because o the higher inex or Blue or F light, Blue light is bent more an the Blue ocus is closest to the lens. The oci corresponing to the F, an C wavelengths are not evenly space ue to the shape o the ispersion curve.

2 Axial or Longituinal Chromatic Aberration Axial chromatic aberration or axial color is a variation o the system ocal length with wavelength. F C = n C C n C C F C F C 0-3 n n C C F C nf nc n C C n n n n F C F C n C C F C C F C F C F C F C F C F C F Axial Chromatic Aberration - Continue F c FC FC C F CF CF FC CF Since Abbe numbers are typically 30-70, the longituinal chromatic aberration o a singlet is.5-3% o the ocal length. The relative orer o the oci is reverse or a negative lens. F ocuses closest to the lens or both a positive an a negative lens. 0-4 Longituinal ocus position: rom ocus Because o the lattening o the ispersion curve, the -C separation tens to be less than the F- separation. F C

3 Axial Chromatic Aberration o a Negative Lens For a negative lens, the Blue or F ocus remains closest to the lens as Blue light has the largest ray bening. O course all o the oci are virtual, but the orer relative to the lens is the same or a negative or positive lens. F C F C 0-5 = The same relationships hol but now the quantities are negative: F c FC C F CF FC CF CF FC Axial or Longituinal Chromatic Aberration The blur associate with the chromatic aberration o the objective lens limits the perormance o an objective. Blur 0-6 To reuce the blur, a small iameter objective lens is require. Since the longituinal aberration is constant or a given, the blur is proportional to the lens iameter. Blur

4 Transverse Axial Chromatic Aberration Transverse axial chromatic aberration measures the image blur sie ue to axial chromatic aberration. r P TA CH 0-7 The rays rom the ege o the pupil are approximately parallel in the vicinity o the ocus. Remember that the axial chromatic is.5-3% o the ocal length an that the iagram is greatly exaggerate. Transverse Axial Chromatic Aberration Transverse axial chromatic aberration measures the image blur sie ue to axial chromatic aberration. Because, the three marginal rays (F, an C) are approximately parallel. TA tanu rp tanu TA CH rp CH Rays rom ege o pupil TA CH U F C 0-8 TA r CH P TA CH epens only on the glass an the pupil raius r P (assumes that the stop is at the lens). TA CH rp

5 Transverse Axial Chromatic Aberration Alternate Derrivation Consier the ege o the lens to be a thin prism o Abbe Number with a eviation an a ispersion. r P TA CH, r Blur TACH r P P rp Blur TACH rp TACH The blur is the prouct o the ispersion an the ocal length. The ray eviation an ispersion grow as the pupil raius normalie by the ocal length. The net result is inepenent o the ocal length. Lateral Chromatic Aberration Longituinal chromatic aberration is chromatic aberration o the marginal ray o the system. Lateral chromatic aberration or lateral color is cause by ispersion o the chie ray. Stop Image Plane C F 0-0 The ege o the lens behaves like a prism. O-axis image points will exhibit a raial color smear. The blur length increases linearly with image height. Each color has a ierent lateral magniication.

6 Achromatic Objective or Doublet Two lens elements with ierent ispersive properties are combine into a single objective lens. Re an blue light are mae to ocus at the same location an a greatly reuce image blur results even with large iameter lenses. 0- Blur Crown Flint Achromatic Doublet The thin lens achromatic oublet corrects longituinal chromatic aberration by combining a positive thin lens an a negative thin lens. Two ierent glasses (, P an, P ) are use. The nominal powers an ocal lengths are or light. FC FC FC FC, at For each lens: i i FCi i i 0- Achromat: 0 FC F C,, at

7 Seconary Chromatic Aberration The solution or the thin lens achromatic oublet result orces the same axial ocus or F an C light (ero primary chromatic aberration), but light can ocus at a ierent location. This resiual is the seconary chromatic aberration or seconary color o the oublet. C C C C C ncc nccc C C C P P C FC FC C P P For an achromat: C PP P P P C n n C C C C n nc n n C C n n C F C F C n P n C F nc C PFC FC an n C P FC FC 0-3 n n C C FC F C Seconary Chromatic Aberration or Seconary Color P P C C P = C C C C C F-C 0-4 Focus shit rom C F C The ocus is probably not the maximum ocus shit rom F an C.

8 Partial Dispersion Ratio an the Abbe Number On a plot o P versus, most glasses lie on a straight line. P P P P The slope o this line is approximately: C, n n F n n n F n n C C C 0-5 Example: BK7 = 64.7 P =.3075 F = P =.937 P P versus Real Glass Data Data or all o the glasses in the Schott Glass Catalog: Partial Dispersion Ratio P,C Abbe Number

9 Singlet versus Doublet Perormance Singlet: Doublet: C C CF C F CF 50 C P CF Primary chromatic aberration o a singlet. 0-7 P C 00 Seconary chromatic aberration o a oublet. The use o the achromatic oublet reuces chromatic ocal length variation by a actor o about 40 over the same ocal length singlet. Excess Power The oublet esign places excess power in the positive element that is cancelle by the negative element. Both elements contribute equal, but opposite, amounts o longituinal chromatic aberration. Just as with the achromatic thin prism, the longituinal chromatic aberration grows slower with the low ispersion glass (positive element) than the high ispersion glass (negative element). Large ierences in the Abbe numbers minimie the excess power an provie better perormance. 0-8 Large Small

Zero Seconary Color In orer to obtain ero seconary chromatic aberration with a oublet, the partial ispersion ratios o the two glasses must be ero.

10 Zero Seconary Color In orer to obtain ero seconary chromatic aberration with a oublet, the partial ispersion ratios o the two glasses must be ero. P P0 C 0 There are some special glass pairs which have ierent Abbe numbers but the same partial ispersion ratio. Unortunately, the ierence in Abbe number is usually small, resulting in an achromatic oublet with signiicant excess power. To correct chromatic aberration at aitional wavelengths more than two glasses are use: 0-9 Apochromat 3 glasses with correction at three wavelengths. Super Apochromat 4 or more glasses an wavelengths. Chromatic Aberration Correction In the early 700s, it was believe that chromatic aberration was unamental an coul not be correcte. Even Isaac Newton mistakenly hel this belie! In the mi-700s, the work o Chester Moor Hall an John Dollon le to the evelopment o the achromatic objective. 0-0 John Dollon , English

Chester Moor Hall then continue to keep his invention secret.

11 The Story o the Achromatic Doublet The original inventor is Chester Moor Hall, a Barrister in Lonon. In 733, he commissione two ierent opticians, Ewar Scarlett an James Mann, to each make one o the lens elements. By chance, both opticians subcontracte the work to the same man, George Bass. Chester Moor Hall then continue to keep his invention secret. 0- Chester Moor Hall , English The Story o the Achromatic Doublet Aroun 750, George Bass tol John Dollon about the achromatic lens he ha mae, or at least the act that ierent glasses have ierent ispersing powers. Dollon then began a series o experiments using ierent types o glass. Dollon s son, Peter, saw the commercial avantages an once they ha mae test lenses, patente the invention in Peter Dollon 73-8, English

12 Achromatic Doublet Patent Chester Moor Hall twice attempte to challenge the patent. He lost his case on the grouns that the person who shoul proit by the invention is the one who beneits the public by it, not one who keeps it locke in his esk rawer. This was a lanmark ecision in patent law that remains in place to toay. Dollon went on to become the ominant manuacturer o telescopes in the late 700s an early 800s. The name Dollon became a synonym or a telescope. 0-3 Rainbows Primary Rainbow Rainbows result rom the combination o reraction, relection an ispersion rom a rainrop. The entering ray is reracte an isperse twice. For the primary rainbow, there is single internal Fresnel relection. Blue light is eviate more than re light. 0-4 Blue Re Rainrops have an inex o reraction o water, n =.33.

13 Rainbows Seconary Rainbow Uner goo viewing conitions, a secon immer rainbow can be seen outsie the primary bow. The seconary rainbow is create when there are two relections insie the rop. The irection o propagation within the rop is reverse. 0-5 Re Blue Observing Rainbows In the primary rainbow, the roplets irecting the re light to the observer are above those that irect the blue light. Because the angle o rotation is opposite, the colors o the seconary rainbow are reverse. The primary rainbow is at an angle o about 4, an the seconary rainbow is at 5. Each observer uses a ierent set o rainrops to view their iniviual rainbow. Light rom the Sun 0-6 Blue Green Re Re Green Blue 5 Observer 4

14 Why is the Sky Blue? Molecules in the atmosphere act as scattering centers or the incient sunlight. The primary scattering mechanism is Rayleigh scattering which has a / 4 epenence. As a result, blue light is preerentially scattere, an the sky appears blue. Scattere Blue Sunlight 0-7 Up-Looking Sensor Why are Sunsets Re? Sunsets are re or the same reason that the sky is blue. The long path length through the atmosphere at sunset epletes the blue an green content o the irect sunlight, leaving res an oranges. 0-8 Sun Blue Scattering Re Sunset

Exam questions OPTI 517. Only a calculator and a single sheet of paper, 8 X11, with formulas will be allowed during the exam.

Exam questions OPTI 517. Only a calculator and a single sheet of paper, 8 X11, with formulas will be allowed during the exam. Exam questions OPTI 517 Only a calculator an a single sheet of paper, 8 X11, with formulas will be allowe uring the exam. 1) A single optical spherical surface oes not contribute spherical aberration.