Advanced Lens Design

Transcription

1 Advanced Lens Design Lecture 9: Field flattening Herbert Gross Winter term 04

2 Preliminary Schedule.0. Basics Paraxial optics, imaging, Zemax handling 8.0. Optical systems Optical systems, raytrace, advanced handling Aberrations I Geometrical aberrations, wave aberrations 4.. Aberrations II PSF, OTF, sine condition, aplanatism, isoplanatism Optimization I Basic principles, merit function setup, optimization in Zemax Optimization II Initial systems, solves, bending, AC meniscus lenses, constraints, effectiveness of variables Structural modifications Zero operands, lens splitting, lens addition, lens removal, material selection Aspheres and freeforms Correction with aspheres, Forbes approach, freeform surfaces, optimal location of aspheres, several aspheres Field flattening Astigmatism and field curvature, thick meniscus, plus-minus pairs, field lenses Chromatical correction Achromatization, apochromatic correction, axial versus transversal, glass selection rules, burried surfaces 3.0. Special correction topics Symmetry, sensitivity, anamorphotic lenses, field lens, telecentricity, stop position 0.0. Higher order aberrations high NA systems, broken achromates, induced aberrations Advanced optimization Local vs global optimization, control of iteration, growing strategies requirements Mirror systems special aspects, double passes, catadioptric systems Diffractive elements color correction, ray equivalent model, straylight, third order aberrations, manufacturing

3 3 Contents. Image shells. Petzval theorem 3. Astigmatism vs field curvature 4. Correcting field curvature

4 4 Field curvature Basic observation: A plane obect gives a curved image plane obect curved image

5 5 Field Curvature Focussing into different planes of a system with field curvature Sharp imaged zone changes from centre to margin of the image field focused at field boundary focused in field zone (mean image plane) focused in center (paraxial image plane) y' receiving planes z image sphere

6 6 Field Curvature and Image Shells Imaging with astigmatism: Tangential and sagittal sharp image shell depending on the azimuth Difference between the image shells: astigmatism Astigmatism corrected: It remains one curved image shell, Bended field: also called Petzval curvature System with astigmatism: Petzval sphere is not an optimal surface with good imaging resolution No effect of lens bending on curvature, important: distribution of lens powers and indices image surfaces sagittal shell tangential shell y' ideal image plane

7 7 Petzval Theorem for Field Curvature Petzval theorem for field curvature:. formulation for surfaces. formulation for thin lenses (in air) Important: - no dependence on bending - no dependence on stop location R ptz R ptz n m ' k n f nk ' nk n n ' r k k k Natural behavior: image curved towards system obect plane Problem: collecting systems with f > 0: If only positive lenses: R ptz always negative R Typical scaling for single lens: R ptz f n.6 optical system real image shell ideal image plane

8 8 Astigmatisms and Curvature of Field Image surfaces:. Gaussian image plane. tangential and sagittal image shells (curved) 3. mean image shell of best sharpness 4. Petzval shell, arteficial, not a good image y' Seidel theory: s' tan s' 3 s' s' 3s' sags' tan s' pet s' s' s' s' ast best s' sag s pet sag pet Astigmatism is difference tan Best image shell ' tan sag tangential surface medium surface best image sagittal surface s' pet s' sag s' tan Petzval surface Gaussian image plane z

9 Petzval Theorem Elementary derivation by a momocentric system of three surfaces: interface surface with r, obect and image surface Consideration of a skew auxiliary axis a s r, a' s' r Imaging condition For the special case of a flat obect gives with n' n n' n s' s r a' Rp, a R p n' n nr surface a' r a auxiliary axis C image s obect s'

10 Petzval Theorem for Field Curvature Goal: vanishing Petzval curvature and positive total refractive power for multi-component systems R f ptz n f h h f Solution: General principle for correction of curvature of image field:. Positive lenses with: - high refractive index - large marginal ray heights - gives large contribution to power and low weighting in Petzval sum. Negative lenses with: - low refractive index - samll marginal ray heights - gives small negative contribution to power and high weighting in Petzval sum

11 Correction of Astigmatism and Field Curvature Different possibilities for the correction of astigmatism and field curvature Two independent aberrations allow 4 scenarious a) bended image plane residual astigmatism b) bended image plane corrected astigmatism c) flattened image plane residual astigmatism d) flattened image plane corrected astigmatism T S y T S y S y T S T z z z z

12 Petzval Shell The Petzval shell is not a desirable image surface It lies outside the S- and T-shell: s' pet 3s' sag s' tan The Petzval curvature is a result of the Seidel aberration theory T S P TSP P S T P S T P S T (a) s 0 ast s s sag tan s s pet sag (b) s 0 ast s s sag tan s s pet pet (c) s ast s s sag tan ( 3) s ( 3) s 0 pet pet (d) s ast s s sag tan s ( s pet ) s sag pet (e) s ast s s sag tan s 0 s pet pet

13 Field Curvature The image splits into two curved shells in the field The two shells belong to tangential / sagittal aperture rays There are two different possibilities for description:. sag and tan image shell. difference (astigmatism) and mean (medial image shell) of sag and tan Paraxial focus Sagittal focus Medial focus field field field T S T S T S z z z Ref: H. Zügge

14 Field Curvature of a Mirror Mirror: opposite sign of curvature than lens Correction principle: field flattening by mirror f' > 0 / R > 0 f' > 0 / R < 0 mirror Gaussian image plane Petzval surface lens Petzval surface Gaussian image plane

15 New Achromate An achromate is typically corrected for axial chromatical aberration The achromatization condition for two thin lenses close together reads F F 0 Petzval shell mean image shell y' The Petzval sum usually is negative and the field is curved R P R P n f f perfect image plane A flat field is obtained, if the following condition is fulfilled F n n F 0 This gives the special condition of simultaneous correction of achromatization and flatness of field n n

16 New Achromate This condition correponds to the requirement to find two glasses on one straight line in the glass map The solution is well known as simple photographic lens (landscape lens) K5 F stop

17 7 Flattening Meniscus Lenses Possible lenses / lens groups for correcting field curvature Interesting candidates: thick mensiscus shaped lenses r nk ' nk n n ' r Rptz k k k k n f n n d r r r d. Hoeghs mensicus: identical radii - Petzval sum zero - remaining positive refractive power F' ( n ) nr d. Concentric meniscus, - Petzval sum negative - weak negative focal length - refractive power for thickness d: r R ptz r d ( n ) d n r r d ( n ) d F' nr ( r d) 3. Thick meniscus without refractive power Relation between radii r r d n n R ptz n r ( n ) d nr d ( n ) 0

18 8 Correcting Petzval Curvature Group of meniscus lenses n n d collimated r r Effect of distance and refractive indices /R pet [/mm] 0 - K5 / d=5 mm 0 - K5 / d=5 mm SF66 / d=5 mm r [mm]

19 9 Correcting Petzval Curvature Triplet group with r r r 3 d/ collimated n n Effect of distance and refractive indices 0 - /R pet [/mm] SF66 / FK3 / SF BK r [mm]

20 0 Flattening Field Lens Effect of a field lens for flattening the image surface. Without field lens. With field lens curved image surface image plane image shell flat image field lens

21 Field Curvature Correction of Petzval curvature in photographic lens Tessar Positive lenses: green n small Negative lenses : blue n large Correction principle: special choice of refractive indices R F n Cemented component: New Achromate Spherical aberration not correctable in the New Achromate

22 Field Curvature Symmetrical system Astigmatism corrected Field curvature remains symmetrical system field curvature T S y' s'

23 Microscope Obective Lens Possible setups for flattening the field Goal: - reduction of Petzval sum - keeping astigmatism corrected Three different classes:. No effort. Semi-flat 3. Completely flat a) single meniscus lense b) two meniscus lenses c) symmetrical triplet D S not plane plane diffraction limit semi plane rel. field d) achromatized meniscus lens e) two meniscus lenses achromatized f) modified achromatized triplet solution

24 Field Curvature 4 Correction of Petzval field curvature in lithographic lens for flat wafer R F n Positive lenses: Green h large Negative lenses : Blue h small F h h F Correction principle: certain number of bulges

25 Field Flatness one waist two waists Principle of multi-bulges to reduce Petzval sum n' r n f p k k k Seidel contributions show principle. bulge. waist. bulge. waist 3. bulge Petz Petz

26 Field Flatness Effect of mirror on Petzval sum Flatness of field for catadioptric lenses 0 -. intermediate image concave mirror. intermediate image