Aberrations in Lens & Mirrors (Hecht 6.3)

Transcription

1 Aberratios i Les & Mirrors (Hecht 6.3) Aberratios are failures to focus to a "poit" Both mirrors ad les suffer from these Some are failures of paraxial assumptio 3 5 θ θ si( θ ) = θ + L 3! 5! Paraxial assumptio assumes oly the first term Error results i poits havig halos aroud it For a image all these add up to make the image fuzzy

2 Why is Light Focus by a Les Why does all the light focus by a les Cosider a curved glass surface with idex o right side Radius of curvature r is cetered at C Let parallel light ray P at height h from axis hit the curvature at T Normal at T is through C formig agle φ to parallel beam Beam is refracted by Sell s law to agle φ to the ormal si( ϕ ) = si( ϕ ) Assumig small agles the si(φ)~φ ad si( ϕ ) = si( ϕ ) or ϕ ϕ From geometry for small agles h h si( φ ) = or φ r r Agle θ the beam makes to the axis is by geometry h θ = φ φ = φ φ = φ r Thus the focus poit is located at f = h si h h r h r ( θ ) θ Thus all light is focused at same poit idepedet of h positio

3 Spherical Aberratios from Paraxial Assumptio Formalism developed by Seidel: terms of the expasio L!! ) si( θ θ θ θ + = Gaussia Les formula r s s = + Now Cosider addig the θ 3 to the les calculatios The the formula becomes = s r s r s s h r s s Higher order terms add more Result ow light focus poit deped o h (distace from optic axis)

4 Types of Spherical Aberratio Logitudial Spherical Aberratio alog axis Trasverse Spherical Aberratio across axis These create a circle of least cofusio at focus Area over which differet parts of image come ito focus Leses also have aberratios due to idex of refractio issues

5 Mirrors ad Spherical Aberratios For mirrors problem is the shape of the mirror Because reflectors geerally ot wavelegth effects Corrected by chagig the mirror to parabola Mirrors usually have short f compared to radius Hece almost all mirror systems use parabolic mirrors

6 Hubble Telescope Example Hubble mirror was ot groud to proper parabola too flat Not foud util it was i orbit Images were terribly out of focus But they kew exactly what the errors Space walk added a les (called costar) to correct this

7 Spherical Aberratio Off axis rays are ot focused at the same plae as the o axis rays Called "skew rays" Pricipal ray, from object through optical axis to focused object Tagetal rays (horizotal) focused closer Sagittal rays (vertical) further away Corrected usig multiple curves o les Aspheric (ot spherical surfaces) shape to give sigle focus poit Or ca use combie two or more spherical surfaces

8 Coma Aberratio Comes from third order si correctio Off axis distortio Results i differet magificatios at differet poits Sigle poit becomes a comet like flare Coma icrease with NA Corrected with multiple surfaces

9 Field Curvature Aberratio All leses focus better o curved surfaces Called Field Curvature positive les, iward curves egative les, outward (covex) curves Reduced by combiig positive & eg leses

10 Distortio Aberratio Distortio meas image ot at paraaxial poits Grid used as commo meas of projected image Picushio: pulled to corers Barrel: Pulled to sides

11 Les Shape Coddigdo Shape Factor q r = r r1 r Shows how aberratios chage with shape 1

12 Idex of Refractio & Wavelegth: Chromatic Aberratio Differet wavelegths have differet idex of refractio Ofte list wavelegth by spectral colour lies (letters) Idex chage is what makes prism colour spread Typical chages 1-2% over visible rage Geerally higher idex at shorter wavelegths

13 Chromatic Aberratio Chromatic Aberratios differet wavelegth focus to differet poits Due to idex of refractio chage with wavelegth Hece focuses rays at differet poits Geerally blue closer (higher ) Red further away (lower idex) Importat for multilie lasers Achromatic leses: combie differet materials whose idex chages at differet rates Compesate each other

14 Lateral Colour Aberratio Blue rays refracted more typically tha red Blue image focused at differet height tha red image

15 Siglet vs Achromat Les Combiig two les sigificatly reduces distortio Each les has differet glass idex positive crow glass egative meiscus flit Give chromatic correctio as well

16 Combied les: Uit Cojugatio Bicovex most distortio Two plaocovex sigificat improvemet Two Achromats, best

17 Materials for Lasers Leses/Widows Stadard visible BK 7 Boro Silicate glass, pyrex For UV wat quartz, Lithium Fluroide For IR differet Silico, Germaium