Principles of Wave Optics - Adaptive Optics for Biological Imaging - page 3

1
Principles of Wave Optics

1.1. Introduction...........................................................................................3
1.2. Physical.Nature.of.Light.......................................................................4
Original.Concepts.of.Light.•.Maxwell's.Equations.and.the.Plane.Wave.
Solutions
1.3. Optical.Paths.through.Materials.and.Free.Space.............................6
Dispersion.and.Refraction. •. Polarization
•. Optical.Path.Length,.Geometric.Rays,.and.Difraction.•.Photons,.
Scattering,.Energy,.and.Momentum
1.4. Analytic.Methods.for.Light.Wave.Propagation.and.Analysis...... 14
Huygens.Wavelets. •. Computer.Simulation.of.Wave.Propagation
1.5. Application.of.Wave.Optics.to.Optical.System.Design................. 18
Ray.Tracing. •. Lagrange.Invariant. •. Maréchal's.Criterion .
• Difraction Limit.• . Depth.of.Field.• . Rayleigh.Range
1.6. Image.Formation.and.Analysis.........................................................24
1.7. Conclusion............................................................................................27

Donald T. Gavel
University of California
at Santa Cruz

1.1 introduction

Adaptive. optics. system. development. requires. a. basic. understanding. of. the. behavior. of. light. both. in.
terms.of.classical.electromagnetic.waves.and.in.terms.of.the.quanta,.or.photon,.phenomena..Key.issues.
relevant. to. system. performance,. such. as. limits. to. sensitivity,. difraction,. transmission,. interference,.
and.so.on,.are.explained.and.calculable.given.a.set.of.fundamental.principles.that.incorporate.the.wave.
theory. of. optics. combined. with. the. quantum. mechanical. interpretation. of. the. wave. ields.. he. wave.
behavior.of.light.is.perhaps.best.explained.using.the.Huygens.wavelet.theory,.which.accurately.predicts.
how.the.waves.propagate.and.add.coherently.in.space.and.time..Ultimately,.however,.our.understand-
ing.of.the.detection.of.light.(and.the.fundamental.signal-to-noise.limits).requires.interpreting.the.wave.
amplitudes.as.probability.amplitudes.for.photon.arrivals.
he.objective.of.this.chapter.is.to.provide.the.reader.with.a.irm.grounding.in.the.physical.theory.
that.best.explains.the.behavior.of.light..As.with.all.theories,.it.is.not.complete..Many.questions.remain,.
which.are.the.subject.of.current.research..However,.armed.with.a.few.fundamental.ideas,.the.practi-
tioner.can.go.a.long.way..We.try.to.minimize.the.oten.cumbersome.mathematical.detail.here.to.get.
right.to.the.key.physical.ideas..(And.too.much.math.can.sometimes.yield.an.undue.sense.of.perfection.
to.a.theory,.distracting.from.the.weaknesses.or.limitations.in.the.assumptions!).here.is.some.neces-
sary. .mathematical. detail,. but. our. emphasis. is. on. the. fundamental. physical. understanding. and. not.
on. the. mathematical. theory.. he. reader. is. referred. to. the. excellent. texts. in. the. ield. for. the. rigorous.
.mathematical.development.
he. wave. optic/quantum. optic. physical. model,. and. the. interaction. with. the. electron. via. quantum.
electrodynamics,. has. been. experimentally. veriied. to. great. accuracy.. he. speed. of. light. in. a. vacuum.

3