Interferometers and Interferometry

Download Interferometers and Interferometry

Post on 06-Nov-2015

4 views

Category:

Documents

2 download

Embed Size (px)

DESCRIPTION

Advanced

TRANSCRIPT

<ul><li><p>Interferometers and Interferometry</p><p> Plane wave interference.</p><p> Spherical wave interference</p><p> Division of Wavefront Interferometers 2-slit interference, Lloyds mirror, biprism</p><p> N-slit interference, Array theorem</p><p> Division of Amplitude InterferometersMach-Zehnder, Michelson, Sagnac</p><p> beamsplitters and multiple reflection artifacts</p><p> Shearing Interferometers. Wedged collimation tester</p><p> Polarization Interferometry</p><p> Temporal Coherence and Fourier Transform SpectroscopyKelvin Wagner, University of Colorado Physical Optics 2011 1</p><p>Plane Waves</p><p>direction cosines of a plane wave</p><p>E(x, y, z) = E0pei2n0</p><p>(x+y+z)= E0pe</p><p>i(kxx+kyy+kzz)</p><p>2 + 2 + 2 = 1 k2x + k2y + k</p><p>2z = n</p><p>2k20 =</p><p>(2n</p><p>0</p><p>)2where k0 = |~k| = 2n/ in medium of index n.</p><p>x</p><p>z</p><p>k</p><p>k-space</p><p>k</p><p>2pin/</p><p>In 2-dimensionsE(x, z; t) = A0pe</p><p>ik0(x sin +z cos )ei2t + cc</p><p>where = sin / and = cos /. 5 1014 Hz .63 106m (HeNe)</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 2</p><p>Interference</p><p>Intensity = |Field|2</p><p>E1(~r, t) = A1p1ei(~k1~r1t) + cc</p><p>E2(~r, t) = A2p2ei(~k2~r2t) + cc</p><p>k-space2pin/</p><p>ko</p><p>kr</p><p>Kg2E Eo r</p><p>E +Eo r2 2</p><p>I(x)</p><p>X</p><p>I(x) = |E1(~r, t) + E2(~r, t)|2= |A1|2 + |A2|2 + A1A2(p1 p2)ei[(~k1~k2)~r+(12)t] + cc= |A1|2 + |A2|2 + A1A2(p1 p2) cos</p><p>[(~k1 ~k2) ~r + (1 2)t</p><p>]Typically require and define the followingp1 p2 = 1 Co-polarized1 2 = 0 Same FrequencyA1A</p><p>2 = a1a2e</p><p>i(12) = a1a2ei amplitude and phase~KG = ~k1 ~k2 = 2 KG Grating wave vectorm = ImaxIminImax+Imin =</p><p>2I1I2</p><p>I1+I2(p1 p2) modulation depth</p><p>I(~r) = I1 + I2 + 2I1I2 cos</p><p>[~Kg ~r + </p><p>]= I0</p><p>(1 +m cos</p><p>[~Kg ~r + </p><p>])Kelvin Wagner, University of Colorado Physical Optics 2011 3</p><p>Spherical Waves</p><p>x</p><p>z eikr</p><p>x</p><p>z e-ikr</p><p>Isophase surfaces are spherical, (r) = const, where r2 = x2 + y2 + z2</p><p>Nonparaxial Spherical Wave</p><p>A(r, t) =Aoreikreit + cc =</p><p>Aoreik</p><p>x2+y2+z2eit + cc</p><p>Paraxial Regimez max(x, y) so that (x2 + y2)/z2 1</p><p>r = z</p><p>1 +</p><p>x2 + y2</p><p>z2 z + x</p><p>2 + y2</p><p>2z</p><p>using1 + = 1 + /2 2/8 + ...</p><p>Paraxial Focusing Sphereical Wave</p><p>A(r, t) = Aoei(kzt)eik</p><p>x2+y2</p><p>2z + cc</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 4</p></li><li><p>Spherical Wave Interference</p><p>I(~r, t) =</p><p>p1(~r ~r1) A1|~r ~r1|ei(k|~r~r1|t) + p2(~r ~r1) A2|~r ~r2|ei(k|~r~r2|t)2</p><p>=A21R21</p><p>+A22R22</p><p>+ 2 (p1(R1) p2(R2))A1R1</p><p>A2R2</p><p>cos [k(R1 R2) ]</p><p>Ri = |~r ~ri|k(R1 R2) = 2n maximak(R1 R2) = (2n + 1) minima</p><p>R1 R2</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 5</p><p>Parabolic Approximation</p><p>A(x, y, z, t) = eik</p><p>x2+y2+z2eitE(R)</p><p>when Z max(x, y) x2+y2z2</p><p> 1 can make Fresnel approxA(x, y, z, t) =</p><p>a0zei(kzt)ei</p><p>k2z (x</p><p>2+y2)</p><p>2 point sources in paraxial regime</p><p>A1(x, y, z, t) =a1zei(kzt)ei</p><p>k2z</p><p>((xd2)</p><p>2+y2</p><p>)</p><p>A2(x, y, z, t) =a2zei(kzt)ei</p><p>k2z</p><p>((x+d2)</p><p>2+y2</p><p>)</p><p>Interference gives intensity x2dx+d24 (x2+dx+d2</p><p>4 )</p><p>I(x, y, z) =a1z</p><p>2 + a2z</p><p>2 = a1a2z2</p><p>ei k2z</p><p>[(xd2)</p><p>2(x+d2)2+y2y2</p><p>]</p><p>=1</p><p>z2</p><p>(|a1|2 + |a2|2 + 2(a1a2) cos</p><p>(k</p><p>2z2dx + (a1a</p><p>2)</p><p>))</p><p>d </p><p>d </p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 6</p><p>Youngs Double Slit</p><p>PointSource</p><p>uniform coneangle </p><p>d/2-d/2</p><p>R1</p><p>R2</p><p>z</p><p>xy</p><p>radiusa</p><p>R1 =</p><p>(x d</p><p>2</p><p>)2+ y2 + z2 R2 =</p><p>(x +</p><p>d</p><p>2</p><p>)2+ y2 + z2 R22R21 = 2xd</p><p>R = R2 R1 = (R2 R1) (R2 +R1)R2 +R1</p><p>=R22 R21R2 +R1</p><p>=2xd</p><p>R2 +R1Fringes strongest near x, y = 0 especially for sources with noticable bandwidth, largepinholes, or large sources</p><p>R2 +R1 2z R = xdz</p><p>I(x, y) =P</p><p>4A2</p><p>4a2</p><p>(I1 + I2 + 2</p><p>I1I2 cos</p><p>(2</p><p>xd</p><p>z</p><p>))Separation of adjacent fringes x = zd varies with wavelength</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 7</p><p>Slit Width</p><p>k = 22xz</p><p>I(x) =</p><p> d+wo/2dwo/2</p><p>I0(1 + cos kx)dx = I0wo +</p><p>(x dwo</p><p>)cos kxdx</p><p>= I0wo + I0wosinc kwo cos kd = I0wo</p><p>(1 + sinc</p><p>2</p><p>2x</p><p>zwo cos</p><p>2</p><p>2x</p><p>zd</p><p>)Visbility= ImaxIminImax+Imin =</p><p>sinc 2 2xz woHigh visibility for w &lt; z</p><p>24x = wmax</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 8</p></li><li><p>Polychromatic Illumination</p><p>Combination of mutually incoherent monochromatic componentsEach component produces a fringe pattern of varying scale</p><p>Sum to get total intensity</p><p>Fringe spacing between maxima s = z/d</p><p>For a center frequency 0and bandwidth fringes will blur out if x &gt; s/4</p><p>x</p><p>x0max</p><p>x x0 0</p><p>t(t)</p><p>0</p><p>2pi</p><p>(t)-(t-)</p><p>0</p><p>2pi</p><p>2pi</p><p>|()|</p><p>00</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 14</p><p>Spectra of the Source</p><p>E() = 12</p><p>E(t)eitdt =1</p><p>2E0( 0) </p><p>ei(t)eitdt</p><p>=1</p><p>2E0( 0) </p><p>n</p><p> (n+1)0n0</p><p>eineitdt =E02( 0) </p><p>n</p><p>ein0sinc0</p><p>Power SpectraP () = |E()|2 = |E0|2 20 sinc 2[( 0)0]</p><p>Spectral width = 2</p><p>= 10</p><p>Coherence time 0Coherence length c0 =</p><p>c =</p><p> =</p><p>2</p><p> = Lc</p><p> Lc Nwaves</p><p>5000A 1A 2mm 5000</p><p>5500A 1250A 2m 4</p><p>6328A 107A = 7.5KHz 40km 6.3 10106328A 6.67 105A = 500MHz .6m 106</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 15</p><p>Source with random phase jumps at equalintervals</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 16</p></li><li><p>Source with random phase jumps at randomintervals</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 17</p><p>Coherence Length</p><p>t = 1/ coherence time = 1/t source bandwithl = ct coherence length</p><p> c =200</p><p>For an OPD = the phase difference = k0</p><p>Fringe pattern</p><p>I() = 2</p><p>i(k0)(1 + cos k0)dk0</p><p>V = ImaxIminImaxr+Imin</p><p>Fringe modulation depth, m (aka visibility) goes to 0 at</p><p>x0 =2</p><p>k=</p><p>c</p><p>= l = ct</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 18</p><p>Fourier Transform Spectroscopy</p><p>L /2</p><p>Mirror</p><p>Translating Mirroron precision rail</p><p>L /21</p><p>2 z</p><p>DetectorI(z)</p><p>Fringes I( ) = 2I1 [1 + ( ) cos (arg (( )))]</p><p>Integrate interference over all wave-numbers to give FT of band shape envelope B(k)</p><p>I(z) =</p><p> 0</p><p>B(k)(1 + cos kz)dk = I0 +1</p><p>2</p><p>B(k)eikzdk</p><p>So by subtracting out DC term, FFT1 fringes we can get spectrum</p><p>B(k) =</p><p>[I(z) I0]eikzdz</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 19</p><p>Coherence Functions for typical laser sources</p><p>Spectrum I() Complex Coherence () |()| Fringe Visibility V () (I1 = I2)True Monochromatic Waves</p><p>I()0 </p><p>V()I() = I0( 0) ei2pi0</p><p>2 Monochromatic Components</p><p>I()1 2</p><p>V()</p><p>( )2 11 2</p><p>I() = I1( 1) + I2( 2) I1I1+I2ei2pi1 + I2I1+I2ei2pi21 4I1I2</p><p>I1+I22 sin2[(2 1) ]</p><p>Doppler Broadened Line</p><p>I() = 2I0D</p><p>ln 2</p><p>pie</p><p>2(0)D</p><p>ln 2</p><p>2</p><p>I()0</p><p>Area=I0ei2pi0e</p><p>hpiD</p><p>2ln 2</p><p>i2e</p><p>hpiD</p><p>2ln 2</p><p>i2</p><p>V()</p><p>where D =0c22k ln 2</p><p>TM</p><p>T = temperature KM = mass of one atom Kgk = Boltzman 1.38 1023 JKTwo Doppler Broadened Lines of equal intensity and equal width</p><p>I()= I0D</p><p>ln 2</p><p>pi</p><p>[e</p><p>2(1)D</p><p>ln 2</p><p>2</p><p>I()1 2</p><p>| cos[(2 1) ]ehpiD</p><p>2ln 2</p><p>i2</p><p>V()</p><p>( )2 11 2 30+e</p><p>2(2)D</p><p>ln 2</p><p>2]</p><p>Lorentzian line</p><p>I()20</p><p>Area=I0 V()</p><p>1/pi</p><p>1I() = I0</p><p>2pil</p><p>1+</p><p>h0L</p><p>i2 r ei2pi0epil epil</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 20</p></li><li><p>Generalized Imaging ModelDiffraction and Aberration Effects</p><p>EntrancePupilObject Image</p><p>xy</p><p>xy</p><p>x0</p><p>zo zi</p><p>S</p><p>S</p><p>xs</p><p>yt</p><p>x</p><p>y</p><p>x</p><p>y</p><p>Exit Pupil withPhase Aberration</p><p>y0h</p><p>Mh</p><p>Abbe TheoryOnly some components of object spectrum are captured by the entrance pupil. Highfrequency components are blocked giving limit s on image resolution.</p><p>Rayleigh TheoryDiffraction effects resulting from finite exit pupil with imposed phase aberrations.</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 21</p><p>Aberrations</p><p>Aberration Free SystemExit pupil illuminated by perfect sphericalwave that focusses toward the geometric imageAberrated Imaging System</p><p>Aberrations can be modeled as a complex phas shiftingplate at the exit pupil.</p><p>P(x, y) = P (x, y)eikW (x,y)W (x, y) is the effective path length errorCan be characterized by peak-to-valley or RMS OPDRMSOPD = 1</p><p>A</p><p>AW (x, y)</p><p>2dA</p><p>CTF in the presence of aberrations</p><p>H(fx, fy) = P (zifx,zify)eikW (zifx,zify)</p><p>Impulse Response</p><p>h(x, y) =1</p><p>(zi)2p</p><p>(x</p><p>zi ,y</p><p>zi</p><p>)F</p><p>{eikW (zifx,zify)</p><p>}</p><p>Peak to Valley OPD</p><p>Reference Sphere</p><p>Off-axis aberrated wavefront</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 22</p><p>Focussing Error</p><p>Phase distribution across exit pupil to focus to ideal image plane zi</p><p>i(x, y) =</p><p>zi(x2 + y2)</p><p>Misfocussed spherical wave focussing to distance za</p><p>A(x, y) =</p><p>za(x2 + y2)</p><p>Path length error</p><p>W (x, y) = k1(A i) = k1</p><p>(1</p><p>za 1zi</p><p>)(x2 + y2) = 1</p><p>2</p><p>(1</p><p>za 1zi</p><p>)(x2 + y2)</p><p>Aperture of width 2w0, maximum error is (f0 =w0zi</p><p>is cutoff for square pupil)</p><p>Wm =12</p><p>(1</p><p>za 1zi</p><p>)w20 W (x, y) =</p><p>Wmw20</p><p>(x2 + y2)</p><p>OTF</p><p>GM(fx, fy) =</p><p>A(fx,fy)eikWm</p><p>w20</p><p>[(x+</p><p>zi2 fx</p><p>)2+(y+</p><p>zi2 fy</p><p>)2(xzi2 fx)2(yzi2 fy)2]dx dy</p><p>A(0,0) dx dy</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 23</p><p>OTF with Focussing Error: Notice phaseshift of spokes</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 24</p></li><li><p>OTF with Focussing Error: 1.25 and 1.5phase of TFFS as edge of nonzero MTF</p><p>=*</p><p>=*</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 25</p><p>Geometrical Calculation of Wave Aberrations</p><p>Consider a ref sphere of radius r centered at Po = (xo, yo, zo) that passes through x, y, zorigin in Exit pupil, and a point P = (x, y, z) on the distorted wavefront.wavefront error</p><p>w = r PPo =x2o + y</p><p>2o + z</p><p>2o </p><p>(xo x)2 + (yo y)2 + (zo z)2</p><p>= zo</p><p>1 +</p><p>x2o + y2o</p><p>z2o ((zo z)</p><p>1 +</p><p>(xo x)2 + (yo y)2(zo z)2</p><p>= zo</p><p>[SS1 + </p><p>x2o + y2o</p><p>2z2o </p><p>x4o + 2x2oy2o + </p><p>y4o8z4o</p><p>] zo</p><p>[SS1 + </p><p>x2o 2xox + x2 + y2o 2yoy + y22z2o</p><p> 18z4o</p><p>{x4o+4x</p><p>2x2o+x4+</p><p>y4o+4y</p><p>2y2o+y4+2(x2ox</p><p>2+</p><p>x2oy2o+x</p><p>2oy</p><p>2+x2y2o+x2y2+y2oy</p><p>2)</p><p>+ 2(4xxoyyo2xx2o2x3xo2xxoy2o 2xxoy22yyox2o2yyox22yy3o2y3yo)}]</p><p>=2xxox2+2yyoy2</p><p>2zo+</p><p>1</p><p>8z4o</p><p>[x4+y4+2x2y2 +4x3xo+4y3yo+4x2yyo+4xxoy2 </p><p>spherical coma6x2x2o6y2y2o2x2y2o 2y2x2o8xxoyyo+4xx3o+4yy3o+4yy3+4xxoy2o+4yyox2o ]</p><p>distortion</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 26</p><p>Rotationally Symmetric System</p><p>The monochrmoatic wave aberrations can be expressed as a Taylor expansion that onlydepends on the vector to the object point ~r = (x, y) and the vector ~ = (x, y) in thepupil plane at which the ray strikes. We can expand the wave aberration function as</p><p>W (xo, yo, x, y) =k,l,m,n</p><p>Wklmnxkylxmyn</p><p>But when the system is rotationally symmetric, simultaneous rotation around the opti-cal axis leaves the wave aberration function W unchanged, and traditionally we rotateto bring the object to be aligned with the y axis (so that ~r = (0, h) for an off axis objectheight h, and ~ = ( sin, cos) ) making it easy to identify y z as the Meridonalplane and x z as the sagittal plane This tells us the wave aberration can only dependon the combination of coordinates invariant to rotation:~r ~r = h2, ~ ~ = 2, and ~ ~r = h cos</p><p>piston defocus lateral mag. 3rd ord piston spherical</p><p>W = W200h</p><p>2 + W020</p><p>2 + W111h cos +</p><p> W400h</p><p>4 + W040</p><p>4</p><p>+W131h3 cos + W222h22 cos2 + W220h22 + W311h3 cos </p><p>coma astigmatism field curvature distortion</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 27</p><p>Converging Spherical Wave Illuminating anAperture: Scaled FT at focus</p><p>Amplitude just after aperture of transmittance t0(x, y)</p><p>u(x, y;d+) = Adeikdei</p><p>k2d(x</p><p>2+y2)t0(x, y)</p><p>Propagate through a distance z is given by a convolution</p><p>hz(x, y) =eikz</p><p>izei</p><p>k2z (x</p><p>2+y2)</p><p>t (x,y)0d</p><p>x</p><p>z0</p><p>u(x, y; 0) = u(x, y;d+) hd(x, y)=</p><p>eikd</p><p>id</p><p> u(x, y;d+)ei k2d[(xx)2+(yy)2]dxdy</p><p>=eikd</p><p>idei</p><p>k2d(x</p><p>2+y2)</p><p> u(x, y;d+)ei k2d(x2+y2)ei2d(xx+yy)dxdy</p><p>Fxy{u(x, y;d+)ei k2d(x2+y2)</p><p>} u=x/dv=y/d</p><p>=A</p><p>id2ei</p><p>k2d(x</p><p>2+y2)T0</p><p>( xd,y</p><p>d</p><p>)Since quadratic phase factors cancel</p><p>I(x, y; 0) =</p><p>(A</p><p>d2</p><p>)2 T0 ( xd,y</p><p>d</p><p>)2Kelvin Wagner, University of Colorado Physical Optics 2011 28</p></li><li><p>Aberrations viewed as wavefront error andvisualized with FT that gives impulse</p><p>response</p><p> Aberrations describe the imperfections of lensesAlos intrinsic aberrations for off-axis free-space focusing</p><p> Can be affected by lens choice, orientation, and alignment Can look at focus or instead viualize with interferometric wavefront Difference between actual and ideal wavefront yields interferogramMany types of interferometers can be used for such optical testing Use ideal component as reference to test unknown component</p><p> or can use CGH reference to test singular optical component</p><p> Can test individual lenses or entire optical system Simplest test is to use lens as a collimator</p><p> compare collimated beam with planar wavefront</p><p>We will explore a library of the primary Seidel aberrationsKelvin Wagner, University of Colorado Physical Optics 2011 29</p><p>Diffraction LimitedPeak: jinc(0)2 = .616</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 30</p><p>Spherical Aberration: .25 waveStrehl Ratio .78</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 31</p><p>Spherical Aberration: .5 waveStrehl Ratio .4</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 32</p></li><li><p>Spherical Aberration: 1 waveStrehl Ratio .09</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 33</p><p>Spherical Aberration: 2 waveStrehl Ratio .05</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 34</p><p>Spherical Aberration: 4 waveStrehl Ratio .026</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 35</p><p>MisFocus: .25 waveStrehl Ratio .95</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 36</p></li><li><p>MisFocus: .5 waveStrehl Ratio .39</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 37</p><p>MisFocus: 1 waveStrehl Ratio .05</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 38</p><p>-1 wave MisFocus partially compensates1 wave Spherical : Strehl Ratio .94</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 39</p><p>1 wave MisFocus partially compensates 1wave</p><p>Spherical -2 waves 5th order spherical : SR .31</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 40</p></li><li><p>Spherical Aberration OTF plots fromliterature</p><p>Optics, Born and WolfIntroduction to the Optical Transfer Function, C.S. Williams and O.A. Becklund, SPIE 1989</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 41</p><p>Field Curvature</p><p>h toto ti</p><p>ti</p><p>h</p><p>Curved Focal Surface</p><p>Petzval</p><p>totito</p><p>ti</p><p>Field curvature even for thin lens. Sag: t</p><p>21</p><p>2</p><p>2fRadius of curvature (ht1) =</p><p>h2</p><p>2 f</p><p>For j surfaces with flat object 0 =, Image curvature given by Petzval sum1j+1</p><p>= nj+1j</p><p>k=0</p><p>(nk+1 nk)ck+1nk+1nk</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 42</p><p>Curvature of Field: 1/4 waveDiffraction limited on-axis, misfocused off-axis</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 43</p><p>Curvature of Field: 1/2 waveDiffraction limited on-axis, misfocused off-axis</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 44</p></li><li><p>Curvature of Field: 1 wave2 wave along diagonal</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 45</p><p>Coma: .25 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 46</p><p>Coma: .5 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 47</p><p>Coma: 1 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 48</p></li><li><p>Coma: 2 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 49</p><p>Coma: 4 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 50</p><p>Coma OTF plots from literatureOptics, Born and WolfIntroduction to the Optical Transfer Function, C.S. Williams and O.A. Becklund, SPIE 1989</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 51</p><p>Astigmatism from Cylindrical lens or laserdiode: .5 wave</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 52</p></li><li><p>1/2 Wave Cylindrical Astigmatismcompensated by 1/2 wave misfocus</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 53</p><p>1/2 Wave Cylindrical Astigmatismcompensated by -1/2 wave misfocus</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 54</p><p>What is Astigmatism?</p><p>Kelvin Wagner, University of Colorado Physical Optics 2011 55</p><p>Geometry of Astigmatism</p><p>TangentialFocus</p><p>SagitalFocus</p><p>Circle of leastConfusion</p><p>Tangential Fan</p><p>Sagital Fan</p><p>PetzvalST</p><p>ParaxialFocal Plane</p><p>object</p><p>Off-a...</p></li></ul>

Recommended

View more >