S1_Optics101

Introduction to CODE V Optics 101 • 1-1 Copyright © 2008 Optical Research Associates 3280 East Foothill Boulevard Pasadena, California 91107 USA (626) 795-9101 Fax (626) 795-0184 e-mail: service@opticalres.com World Wide Web: http://www.opticalres.com Copyright © 2008 Optical Research Associates Introduction to CODE V Training: Day 1 “Optics 101” Digital Camera Design Study User Interface and Customization Section 1 Optics 101 (on a Budget) Introduction to CODE V Optics 101 • 1-2 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-3 Goals and “Not Goals” • Goals: – Brief overview of basic imaging concepts – Introduce some lingo of lens designers – Provide resources for quick reference or further study • Not Goals: – Derivation of equations – Explain all there is to know about optical design – Explain how CODE V works Introduction to CODE V Training, “Optics 101,” Slide 1-4 Sign Conventions • Distances: positive to right • Curvatures: positive if center of curvature lies to right of vertex • Angles: positive measured counterclockwise • Heights: positive above the axis t >0 t < 0 VC c = 1/r < 0 V C c = 1/r > 0 θ > 0 θ < 0 Introduction to CODE V Optics 101 • 1-3 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-5 Light from Physics 102 • Light travels in straight lines (homogeneous media) • Snell’s Law: n sin θ = n’ sin θ’ • Paraxial approximation: – Small angles: sin θ~ tan θ ~ θ; and cos θ ~ 1 – Optical surfaces represented by tangent plane at vertex • Ignore sag in computing ray height • Thickness is always center thickness – Power of a spherical refracting surface: 1/f = φ = (n’-n)*c – Useful for tracing rays quickly and developing aberration theory Introduction to CODE V Training, “Optics 101,” Slide 1-6 Cardinal Points Illustrated • Effective Focal Length (EFL) = distance from principal point to focal point P1F1 F2 EFLEFL n n n’ Introduction to CODE V Optics 101 • 1-4 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-7 Cardinal Points • 6 important points along the axis of an optical system – 2 focal points (front and back): Input light parallel to the axis crosses the axis at focal points F and F’ – 2 principal points (primary and secondary): Extend lines along input ray and exiting focal ray; where they intersect defines principal “planes” which intersect the axis at the principal points – 2 nodal points (first and second): Rays aimed at the first appear to emerge from the second at the same angle – “First” points defined by parallel rays entering from the right; “second” points defined by parallel rays entering from the left Introduction to CODE V Training, “Optics 101,” Slide 1-8 Aperture Stop • Aperture stop: determines how much light enters the system • 2 special rays – Marginal ray: from on-axis object point through the edge of the stop – Chief ray: from maximum extent of object through the center of the stop Aperture Stop Chief ray Marginal ray Introduction to CODE V Optics 101 • 1-5 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-9 Pupils and the Aperture Stop • Pupils – Entrance pupil: image of aperture stop viewed from object space – Exit pupil: image of aperture stop viewed from image space Entrance pupil location Exit pupil location Entrance pupil diameter (EPD) Aperture Stop Introduction to CODE V Training, “Optics 101,” Slide 1-10 Specifying the Aperture • EPD = Entrance pupil diameter • NAO = Numerical aperture in object space (finite object) • NA = Numerical aperture in image space • f/# = EFL/EPD • Note: some NAO systems will not fill a physical aperture stop (common in photonics systems). You still must specify a stop surface. Introduction to CODE V Optics 101 • 1-6 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-11 Specifying the Pupil Object H H' Image THI S0 L Entrance pupil EPD θ NAO = n sinθ θ = tan-1(EPD / 2L) NA = NAO / RED = n' sinθ' FNO = 1 / (2×NA) θ' RED = – H' / H • Infinite object: – ƒ/# = EFL/EPD – NAO not valid Introduction to CODE V Training, “Optics 101,” Slide 1-12 Same Triplet, Different f/#’s f/3 f/4 f/8 “Faster” “Slower” Introduction to CODE V Optics 101 • 1-7 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-13 Field Definition • Field definition describes how much of the object you image • Specify object angle, object height (finite object), or image height Object Image Object height (YOB) Object angle (YAN) Image height (YIM) Entrance pupil L YOB = - YIM/RED YOB = -L*tan(YAN) Introduction to CODE V Training, “Optics 101,” Slide 1-14 Aberrations • Perfect imaging: point on object maps to point on the image, for all points on object and all rays through the aperture stop. • Aberrations: deviations from perfect imaging • “1st order” aberrations: – Defocus: wrong image location – Tilt: wrong image orientation • “3rd order” aberrations: – Used in classical aberration theory • Spherical aberration • Coma • Astigmatism • Field Curvature • Distortion Introduction to CODE V Optics 101 • 1-8 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-15 Spherical Aberration • Focal length (EFL) varies with aperture height – Only aberration on-axis – No field dependence Through-focus Spot Diagram Marginal ray focus Paraxial ray focus Introduction to CODE V Training, “Optics 101,” Slide 1-16 Coma • Magnification varies with aperture – Rays through edge of aperture hit image at different height than rays through center of aperture Chief ray Marginal rays Introduction to CODE V Optics 101 • 1-9 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-17 Astigmatism • Sagittal (x-axis) and tangential (y-axis) ray fans have different foci Through-Focus Spot Diagram Tangential focus Sagittal focus Introduction to CODE V Training, “Optics 101,” Slide 1-18 Field Curvature • Planar object forms curved image – Depends on index of refraction of lens material and lens power Best image is on a curved plane Introduction to CODE V Optics 101 • 1-10 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-19 Distortion • Image magnification depends on image height – Image is misshapen, but focus isn’t changed Paraxial chief ray location Real chief ray location Vertical FOV Horizontal FOV Barrel Distortion Pincushion Distortion Introduction to CODE V Training, “Optics 101,” Slide 1-20 Qualitative Effects of Aberrations on Image Quality • Aberrations may cause uniform blur over the field: – Defocus – Spherical aberration • Aberrations may cause field-dependent blur: – Tilt – Coma – Astigmatism – Field curvature – Distortion Image with Spherical Aberration Image with Field Curvature Introduction to CODE V Optics 101 • 1-11 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-21 Ray Aberration Curves • Vertical axis: distance on image plane between chief ray and current ray • Horizontal axis: relative height of ray in aperture stop (or entrance/exit pupil) Chief ray y(ρ=1) y(ρ= -0.75) Image plane Aperture stop ρ=1 ρ= -0.75 y z 0 1-1 10 Ray error (mm) -0.75 y(ρ=1) y(ρ= -0.75) Tangential (y-fan) Sagittal (x-fan) Relative Aperture ρ Ray error (mm) Introduction to CODE V Training, “Optics 101,” Slide 1-22 Chromatic Aberration • Index is function of wavelength: n = n(λ) • Abbe number describes the dispersion: Vd = (nd –1)/(nF –nc) – λd = 587.6 nm (yellow) – λF = 486.1 nm (blue) – λc = 656.3 nm (red) • Small Vd (Vd ~ 20 - 50): very dispersive, colors spread a lot • Large Vd (Vd ~ 55 - 90): less dispersion Index vs. λ, NBK7_Schott 1.5 1.505 1.51 1.515 1.52 1.525 1.53 1.535 750 700 650 600 550 500 450 400 Wavelength λ (nm) In d e x o f R e fr a ct io n n Introduction to CODE V Optics 101 • 1-12 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-23 Rays and Waves • Rays are normal to wavefront • Waves diffract at apertures and can interfere • Rays can image perfectly; waves can’t due to diffraction at apertures – A point images to Airy disk – Diffraction-limited spot size (diameter) = 2.44 λ f/# (microns) 2.44 λ f/# Intensity at image plane Introduction to CODE V Training, “Optics 101,” Slide 1-24 Modulation Transfer Function (MTF) • Start with black and white bars (or sinusoid) with specified frequency. • Frequency in “lines/mm,” where “lines” = “line pairs” (1 black line + 1 white line)= cycle • Modulation = contrast – Imax = maximum intensity – Imin = minimum intensity – for object, contrast = 1 (pure black and white) minmax minmax II IIContrastMTF + −== Introduction to CODE V Optics 101 • 1-13 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-25 MTF M T F Object: Spatial Frequency (cycles/mm) X T S (R) 1 0 Intensity along image slice Object: 1 0 1 0 Image 1: Image 1 Position Image 2 Image 2: MTF depends on target orientation: (direction of variation of intensity) S = Sagittal (a.k.a. R = Radial) or T = Tangential Y X Y Introduction to CODE V Training, “Optics 101,” Slide 1-26 MTF (cont.) • Image is not perfect; contrast drops due to: – Aberration – Diffraction – Vignetting • Varies with: – Field point considered – Orientation of target (radial or tangential) Introduction to CODE V Optics 101 • 1-14 Copyright © 2008 Optical Research Associates Introduction to CODE V Training, “Optics 101,” Slide 1-27 Gaussian Beams W Xo,Yo X,Y W = W(Z) Wo WAIST (Z = 0) Z θ w0 is 1/e2 spot radius at waist w(z) is 1/e2 spot radius at distance z from the waist Beam wavefront is planar at waist θ is laser divergence angle = λ/πw0 θ λπ= w0 Introduction to CODE V Training, “Optics 101,” Slide 1-28 References for Optics Library • General references – R. Fischer, Optical System Design – J. Greivenkamp, Field Guide to Geometrical Optics – D. Malacara, Optical Shop Testing – R. Shannon and B. Tadic, The Art and Science of Optical Design – W. Smith, Modern Optical Engineering – W. Smith, Modern Lens Design • Classics (may be difficult to locate) – R. Kingslake, Lens Design Fundamentals – Rudolf Kingslake, Applied Optics and Optical Engineering, Vol. 1-5 – R. Shannon and J. Wyant, Applied Optics and Optical Engineering, Vol. 6-10 – W. Welford, Symmetrical Optical Systems – U.S. Government, Mil. Handbook 141