Lens Design II. Lecture 5: Field flattening Herbert Gross. Winter term

Transcription

1 Les Desig II Lecture 5: Field flatteig Herbert Gross Witer term 07

2 Prelimiary Schedule Les Desig II Aberratios ad optimizatio Repetitio 3.0. Structural modificatios Zero operads, les splittig, les additio, les removal, material selectio Aspheres Correctio with aspheres, Forbes approach, optimal locatio of aspheres, several aspheres Freeforms Freeform surfaces, geeral aspects, surface descriptio, quality assessmet, iitial systems Field flatteig Astigmatism ad field curvature, thick meiscus, plus-mius pairs, field leses Chromatical correctio I Achromatizatio, axial versus trasversal, glass selectio rules, burried surfaces Chromatical correctio II Secodary spectrum, apochromatic correctio, aplaatic achromates, spherochromatism Special correctio topics I Symmetry, wide field systems, stop positio, vigettig 9.. Special correctio topics II Telecetricity, moocetric systems, aamorphotic leses, Scheimpflug systems Higher order aberratios High NA systems, broke achromates, iduced aberratios Further topics Sesitivity, sca systems, eyepieces 5.0. Mirror systems special aspects, double passes, catadioptric systems 3.0. Zoom systems Mechaical compesatio, optical compesatio Diffractive elemets Color correctio, ray equivalet model, straylight, third order aberratios, maufacturig Realizatio aspects Toleracig, adustmet

3 3 Cotets. Image shells. Petzval theorem 3. Astigmatism vs field curvature 4. Correctig field curvature

4 4 Field curvature Basic observatio: A plae obect gives a curved image plae obect curved image

5 5 Curved Detector Surfaces Huma eye Detector of NASA s Kepler space telescope Also small, curved CMOS image detectors have recetly become available for cosumer optics. Ref.: D. Ochse

6 6 Field Curvature Focussig ito differet plaes of a system with field curvature Sharp imaged zoe chages from cetre to margi of the image field focused at field boudary focused i field zoe (mea image plae) focused i ceter (paraxial image plae) y' receivig plaes z image sphere

7 7 Field Curvature ad Image Shells Imagig with astigmatism: Tagetial ad sagittal sharp image shell depedig o the azimuth Differece betwee the image shells: astigmatism Astigmatism corrected: It remais oe curved image shell, Beded field: also called Petzval curvature System with astigmatism: Petzval sphere is ot a optimal surface with good imagig resolutio No effect of les bedig o curvature, importat: distributio of les powers ad idices image surfaces sagittal shell tagetial shell y' ideal image plae

8 8 Petzval Theorem for Field Curvature Petzval theorem for field curvature:. formulatio for surfaces. formulatio for thi leses (i air) Importat: - o depedece o bedig - o depedece o stop locatio R ptz R ptz m ' k f k ' k ' r k k k Natural behavior: image curved towards system obect plae Problem: collectig systems with f > 0: If oly positive leses: R ptz always egative R Typical scalig for sigle les: R ptz f.6 optical system real image shell ideal image plae

9 9 Field Curvature Special visualizatio of field curvature i case of a telecetric ray path real image shell y image plae telecetric chief rays z Ref: J. Sasia

10 0 Astigmatisms ad Curvature of Field Image surfaces:. Gaussia image plae. tagetial ad sagittal image shells (curved) 3. mea image shell of best sharpess 4. Petzval shell, arteficial, ot a good image y' Seidel theory: s' ta s' 3 s' s' 3s' sags' ta s' pet s' s' s' s' ast best s' sag s pet sag pet Astigmatism is differece ta Best image shell ' ta sag tagetial surface medium surface best image sagittal surface s' pet s' sag s' ta Petzval surface Gaussia image plae z

11 Petzval Theorem Elemetary derivatio by a momocetric system of three surfaces: iterface surface with r, obect ad image surface Cosideratio of a skew auxiliary axis a s r, a' s' r Imagig coditio For the special case of a flat obect gives with ' ' s' s r a' Rp, a R p ' r surface a' r a auxiliary axis C image s obect s'

12 Petzval Theorem for Field Curvature Goal: vaishig Petzval curvature ad positive total refractive power for multi-compoet systems R f ptz f h h f Solutio: Geeral priciple for correctio of curvature of image field:. Positive leses with: - high refractive idex - large margial ray heights - gives large cotributio to power ad low weightig i Petzval sum. Negative leses with: - low refractive idex - samll margial ray heights - gives small egative cotributio to power ad high weightig i Petzval sum

13 Correctio Optios for Field Curvature Petzval curvature thi leses: thick leses ad positive total refractive power Solutios:. Mirrors: formal < 0, positive cotributio to field curvature. Negative field les ear image plae with mior effect of image formatio: h = 0 3. Thick mesicus leses with positive cotributio to field curvature 4. Combiatio of leses with P-N-P power positive ( large) - egative ( small) - positive ( large) ptz f R f h h f ' ' r r d f r R k k k k k k ptz 0 R ptz f mirror 0 r r d R ptz

14 Correctio of Astigmatism ad Field Curvature Differet possibilities for the correctio of astigmatism ad field curvature Two idepedet aberratios allow 4 scearious a) beded image plae residual astigmatism b) beded image plae corrected astigmatism c) flatteed image plae residual astigmatism d) flatteed image plae corrected astigmatism T S y T S y S y T S T z z z z

15 5 Petzval Shell The Petzval shell is ot a desirable image surface It lies outside the S- ad T-shell: s' pet 3s' sag s' ta The Petzval curvature is a result of the Seidel aberratio theory T S P TSP P S T P S T P S T (a) s 0 ast s s sag ta s s pet sag (b) s 0 ast s s sag ta s s pet pet (c) s ast s s sag ta ( 3) s ( 3) s 0 pet pet (d) s ast s s sag ta s ( s pet ) s sag pet (e) s ast s s sag ta s 0 s pet pet

16 Field Curvature The image splits ito two curved shells i the field The two shells belog to tagetial / sagittal aperture rays There are two differet possibilities for descriptio:. sag ad ta image shell. differece (astigmatism) ad mea (medial image shell) of sag ad ta Paraxial focus Sagittal focus Medial focus field field field T S T S T S z z z Ref: H. Zügge

17 Field Curvature of a Mirror Mirror: opposite sig of curvature tha les Correctio priciple: field flatteig by mirror f' > 0 / R > 0 f' > 0 / R < 0 mirror Gaussia image plae Petzval surface les Petzval surface Gaussia image plae

18 New Achromate A achromate is typically corrected for axial chromatical aberratio The achromatizatio coditio for two thi leses close together reads F F 0 Petzval shell mea image shell y' The Petzval sum usually is egative ad the field is curved R P R P f f perfect image plae A flat field is obtaied, if the followig coditio is fulfilled F F 0 This gives the special coditio of simultaeous correctio of achromatizatio ad flatess of field

19 New Achromate This coditio correpods to the requiremet to fid two glasses o oe straight lie i the glass map The solutio is well kow as simple photographic les (ladscape les) K5 F stop

20 0 New Achromate This coditio correspods to the requiremet to fid two glasses o oe straight lie through the origi i the glass map 0 Abbe umber PSK5 LAK33 K5 LLF LASF40 SF idex Examples: K5 / PSK5: = SF / N-LASF40: = LLF / LAK33: = The solutio is well kow as simple photographic les (ladscape les) LLF LAK33 stop Origi

21 Flatteig Meiscus Leses Possible leses / les groups for correctig field curvature Iterestig cadidates: thick mesiscus shaped leses r k ' k ' r Rptz k k k k f d r r r d. Hoeghs mesicus: idetical radii - Petzval sum zero - remaiig positive refractive power F' ( ) r d. Cocetric meiscus, - Petzval sum egative - weak egative focal legth - refractive power for thickess d: r R ptz r d ( ) d r r d ( ) d F' r ( r d) 3. Thick meiscus without refractive power Relatio betwee radii r r d R ptz r ( ) d r d ( ) 0

22 Field Flatteig by Meiscus Les Compesatig the field curvature of a achromate by a meiscus les Meiscus with power F = 0 ad ( ) t R r r t ( ) ptz Variatio of curvature ad thickess Optimal thickess decreases for stroger meiscus bedig sag of field curvature i mm Orietatio of meiscus ot idetical for larger t-values: egative R more beeficial correctio lie with z = thickess t meiscus i mm

23 3 Correctig Petzval Curvature Group of meiscus leses d collimated r r Effect of distace ad refractive idices /R pet [/mm] 0 - K5 / d=5 mm 0 - K5 / d=5 mm SF66 / d=5 mm r [mm]

24 4 Correctig Petzval Curvature Triplet group with r r r 3 d/ collimated Effect of distace ad refractive idices 0 - /R pet [/mm] SF66 / FK3 / SF BK r [mm]

25 5 Flatteig Field Les Effect of a field les for flatteig the image surface. Without field les. With field les curved image surface image plae image shell flat image field les

26 Field Leses Field les: i or ear image plaes Iflueces oly the chief ray pupil shifted to meet the ext sub-system Reductio of system diameter Critical: cougatio to image plae, surface errors sharply see margial ray chief ray field les i itermediate image plae les L les L shifted pupil origial pupil Ref: B. Böhme 6

27 Field Curvature Correctio of Petzval curvature i photographic les Tessar Positive leses: gree small Negative leses : blue large Correctio priciple: special choice of refractive idices R F Cemeted compoet: New Achromate Spherical aberratio ot correctable i the New Achromate

28 Field Curvature Symmetrical system Astigmatism corrected Field curvature remais symmetrical system field curvature T S y' s'

29 Microscope Obective Les Possible setups for flatteig the field Goal: - reductio of Petzval sum - keepig astigmatism corrected Three differet classes:. No effort. Semi-flat 3. Completely flat a) sigle meiscus lese b) two meiscus leses c) symmetrical triplet D S ot plae plae diffractio limit semi plae rel. field d) achromatized meiscus les e) two meiscus leses achromatized f) modified achromatized triplet solutio

30 Field Curvature 30 Correctio of Petzval field curvature i lithographic les for flat wafer R F Positive leses: Gree h large Negative leses : Blue h small F h h F Correctio priciple: certai umber of bulges

31 Field Flatess oe waist two waists Priciple of multi-bulges to reduce Petzval sum ' r f p k k k Seidel cotributios show priciple. bulge. waist. bulge. waist 3. bulge Petz Petz

32 Field Flatess Effect of mirror o Petzval sum Flatess of field for catadioptric leses 0 -. itermediate image cocave mirror. itermediate image