06 Instruments and Optical Invarientecee.colorado.edu/~ecen5616/WebMaterial/06 Instruments and...

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Instruments and the Optical Invariant

• Telescopes• M=1/Mθ• Microscopes and eye pieces• Camera• Fiber Optics• Spectrometers• Optical Disk

• media • laser isolation• optical head• optical system with servo signal

• Optical Invariant

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Example: The TelescopeKeplerian

Shown in the afocal geometry (d=f1+f2). Relaxed eye focuses at ~1m, thus telescope are usually not afocal. Analysis simpler, however.

Definition of angular magnification

Via similar triangles

This is both important and fundamental.

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Example: The TelescopeGalilean

yu

h10

h1-h1/f1

h1- h1(f1+f2)/f1-h1/f1 – (h1-h1(f1+f2)/f1)/f2=0

h1- h1(f1+f2))/f1 = -h2-h1/f1 – (h1-h1(f1+f2)/f1)/f2

M = h2/h1 = -f2/f1

() =h1f2/f1 -h2 = h1f2/f1

But f2 is negative so M>0

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Example: The TelescopeGalilean

Note that formula is identical to Keplerian.This is the advantage of the sign convention.

hh

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Reflective Telescopes

Chromatic aberration is very small with mirrors, transmission can be very high, light weight

Magnification same as Keplerian / Galilean

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Magnifier - through anglesUseful for infinite conjugates

For a equal focal lengths, fe, visual magnification should beproportional to ratio of angles

Via similar triangles

via lens power equation

Dnp=10 inch, shortest distance an eye can focus to

-tm

Dnp

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Compound Microscope

Focus by moving object relative toboth lenses and stop

L-Tube length

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Visual magnification is product of linear mag of objective and mag of eyepiece:

Microscope

Remember M=-xi/F (thin lens)

Standard Near Point is 10 inches (254mm)

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Eye PiecesUsed with microscope and telescopes

HuygensRamsden

Kellner

Can get Zemax examples

If standard NP=10 inches a 10x eye piece would have a F=1 inch

Cheap but bad eye relief Cheap but better eye relief (common)

Achromatic Ramsden, wide field

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More Eye Pieces

Orthoscopic Plossl (symmetrical)

Erfle Most common wide field EP

Better image qualityBetter image quality over field

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Camera

SLR – Single Lens Reflex Camera

35mm Camera• wide range of F available cheaply• 46.5mm from mount to film plane• Nikon, Canon major vendors• Zeiss, Leica, Tamron, Tokina, Scheider, etc• Image size: 24 mm×36 mm.

Medium and Large Format CameraHasselblad (Zeiss), Mammia56.5 x 56.5mm film sizes plus110mm F2, Hasselblad ~ 5-6kBFL=74.9mm

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Film (Field) sizes

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Wide AngleF= 6mm-40mmFOV 50-220°

Standard

StandardF= 50-65mmFOV 40-50°

1893, Fewest # elements with 3rd ab 0

1840, portrait lens

Camera Lenses

You can find Zemaxexamples online

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Nikon AF Micro-Nikkor105mm f/2.8

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Hasselblad 80mm, f/2.8

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Fiber Optics

−−

−=== cca nnNA θθθ 211 cos1sinsin

Multimode step index

Single mode

Multimode gradient index

22

21

2

1

21 1 nn

nnnNA −=⎟⎟⎠

⎞⎜⎜⎝

⎛−=

What is the NA that the fiber can accept/ send out ? Core is n1 and cladding is n2

Ex: n1=1.475, n2=1.46 then NA=.21 and θa=12 degrees

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IS

m sinsin ±=λα

α is the angle diffractedλ is the wavelength of lightm is the order numberI is the incident angle + sign is for transmission, - is for reflective gratingS – is the period of the grating (spacing of the grating lines)

Spectrometersusing gratings

Grating equation

Since angle depends on λ, can use to measure wavelength

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Spectrometersusing gratings

The dispersion of the grating is dθ/dλ (differentiating the grating equation)

dθ/dλ = m/(S cosθ)

The effective width of a line is equal to Δα=2π/N, where N is the number of grating lines illuminated (assuming the Aperture Stop is the grating) Δα can be written as (kS/2) (sinθ – sinθi) or (kS/2) cosθ (Δθ).

This can be written asdθmin = 2λ/(NS cosθm)This is the FULL angular width of a line due to instrument broadening

Plug this into above equation and solve for dλ results inλ/dλmin = mN = R( resolving power) = NS(sinα ± sinI)/λ

Or dλmin = λ/mN6in wide grating at 15,000lines/in in 2nd order will resolve180,000 lines, at 540nm dλ = 0.003nm

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Optical disks• Probably the largest volume optical system ever –

CD,DVD, BD– 10’s of million devices per year

• First video disk in early 1970 – killed (12 inch)• CD mid 1970’s

– First CD-R from Sony cost $15,000– Current OEM price for CDROM is ~8 dollars

– ~10 Billion disks per year• CD price are <20 cents a disk with 10 cents being IP royality• DVD’s maybe 50 cents

– Record and read by focusing beam to diffraction limited spot andchanging reflectivity or polarization state of media

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Focus ServoFx>Fy

A+D-(B+C)Or (AD-BC)

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Tracking Servo

If NA of lens is > 0.5λ/p orders will overlap

Where p is grating period (track width)

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Optical Head Write Once Drive

• MO has polarizer between PBS and toric lens• Data signal is transitions for bright state to dark state. RLL codes are used to make sure timing stays sync’ed

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Laser Feedback Elimination

“Optical recording”, Alan Marchant, Addison Wesley

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Recordable Media

Examples include: InSeTe and GeSeTe and many others flavors

Phase Change: Sole survivor

Magneto-optical materials

Being considered for next gen hard drives

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Optical InvariantAt image/object plane (special case)

Paraxial Snell’s Law

Triangles

Substitute into M

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Optical InvariantAt image/object plane (special case)

Invariant – this expression has the same value everywhere in the optical system.

At an object or image plane the invariant is equal to the index times the object/image height times the half convergence/divergence angle of the axial beam

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Optical invariantaka Lagrange or Helmholtz invariant

is conserved everywhere

At a general surface anywhere in the optical system the invariant is expressed as

The 3D version for throughput is that the product of the object/image area times the solid angle of collection is invariant

Write the paraxial refraction equations for the marginal ray (PMR)and chief or pupil ray (PPR):

With a bit of algebra:

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Basic Definitions

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Examples• Given object and image slopes and object height

can find height of image.– uo = .333, ui=-0.04755, h=20mm– M=h’/h => h’= (20)(0.333)/(-0.04755)= -14.0187mm

• Image height for lens with object at infinity– Y for axial ray is 0, slope of u is zero, up is half FOV

INV = h’n’u’ = -y1nup

h’ = -upy1/u’ for n=n’F= -y1/u’ soh’ = upF or F tanup for non paraxial case

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Optical invariantaka Lagrange or Helmholtz invariant

Using the invariant, at the object (or image) of limited field diameter L: y = 0, = edge of field, u = maximum ray angle

Thus we have found the information capacity of the opticalsystem, aka the space-bandwidth product:

Rayleigh Resolution(NA = 0.6λ/Δr)

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Question

If an object that is 1 cm2 with 1 sr of solid angle is images to 2cm2 area,

What is the solid angle of this image ?

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Homework #2

Available at the website under homework

http://ecee.colorado.edu/~ecen4616http://ecee.colorado.edu/~ecen5616

Due in 2 weeks