optics – reu lecture 2009 richard 1 reu lecture optics and optical design erik richard...

Optics – REU Lecture 2009 Richard 1

REU Lecture

Optics and Optical Design

Erik [email protected]

303.735.6629


Outline

•Brief Review: Nature of Light (Electromagnetic Radiation)–Propagation of E&M waves–Interaction with matter–Wave-particle duality

• Brief Review: Optics Concepts- Refraction - Reflection- Diffraction grating characteristics–Imaging characteristics of lenses and mirrors–Detectors

•Instrument Design and Function–Drawings–Block Diagram–Mechanisms


Classical Definition: Energy Propagating in the form of waves– Many physical processes give rise to E&M radiation including

accelerating charged particles and emission by atoms and molecules.

Nature of Light (Electromagnetic Radiation)


Electromagnetic Spectrum

• Velocity, frequency and wavelength are related: c=where: • c=3x108 m/sec is the velocity in vacuum and are the wavelength and frequency respectively

• Electromagnetic radiation is typically classified by wavelength:


Nature of Light: Wave-Particle Duality

• Light behaves like a wave– While propagating in free space (e.g. radio waves)

– On a macroscopic scale (e.g. while heating a thermometer)

– Demonstrates interference and diffraction effects

• Light behaves as a stream of particles (called photons)– When it interacts with matter on a microscopic scale

– Is emitted or absorbed by atoms and molecules

• Photons:– Travel at speed of light

– Possess energy: E=h=hc/• Where h=Planck’s constant h=6.63e-34 Joule hz-1

• A visible light photon ( =400 nm) has=7.5 x 1014 hz and E=4.97 x 10-19 J


Nature of Light: Photon Examples

Atoms and Molecules Photoelectric Effect

The nature of the interaction depends on photon wavelength (energy).

Electron kinetic energy: K.E.=h-W. W is the work function (depth of the ‘potential well’) for electrons in the

surface. 1ev=1.6x10-19J


The hotter and higher layers produce complex EUV (10-120 nm) emissionsdominated by multiply ionized atoms with irradiances in excess of the photospheric Planck distribution.

A closer look at the Sun’s spectrum

Note log-scale for irradiance


Alt

itu

de (

km)

Atmospheric absorption of solar radiation

Altitude “contour” for attenuation bya factor of 1/e

~99% solar radiationpenetrates to the

troposphere

I(km) = 37% x Io

troposphere

stratosphere

Solar FUV and MUV radiation is the primary source of energy for earth’s upper atmosphere.

O3

N2, O, O2


Atmospheric Absorption in the Wavelength

Range from 1 to 15 m


Black Body Radiation

• An object radiates unique spectral radiant flux depending on the temperature and emissivity of the object. This radiation is called thermal radiation because it mainly depends on temperature. Thermal radiation can be expressed in terms of black body theory.

Black body radiation is defined as thermal radiation of a black body, and can be given by Planck's law as a function of temperature T and wavelength


Blackbody Radiation Curves

€

u(λ ,T) =2hc 2

λ 5

1

ehc

λkT −1

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟


Black body radiation

• Planck distributions

Hot objects emit A LOT moreradiation than cool objects

The hotter the object, theshorter the peak wavelength

I (W/m2) = x T4

T x max = constant


Solar Spectral Irradiance

SORCE Instruments measure total solar irradiance and solar spectral irradiance in the 1 -2000 nm wavelength range.


Solar Cycle Irradiance Variations

The FUV irradiance varies by ~ 10-100% but the MUV irradiance varies by ~ 1-10% during an 11 year solar cycle.


• Solar irradiance modulated by presence of magnetic structures on the surface of the Sun……Solar Rotation (short) Solar Cycle (longer)

• The character of the variability is a strong function of wavelength.

Greatest absolute variability occurs in mid visible

Greatest relative variability occurs in the ultraviolet.

Solar variability across the spectrum


Atmospheric Observation Modes

Direct Solar Radiation


Functional Classes of Sensors


Element of optical sensors characteristics

Sensor

Spectral bandwidth () Resolution ()

Out of band rejectionPolarization sensitivity

Scattered light

Detection accuracySignal to noiseDynamic range

Quantization levelFlat fielding

Linearity of sensitivityNoise equivalent power

Field of viewInstan. Field of view

Spectral band registrationAlignments

MTF’sOptical distortion

Spectral Characteristics Radiometric Characteristics Geometric Characteristics


refractive index = speed of light in vacuumspeed of light in medium

Glass : n =1.52Water : n=1.33Air : n=1.000292

As measured with respect to the surface normal :

angle of incidence = angle of reflection

Snell 's law :

nsinθ = n'sinθ '

Reflection and refraction


Critical angle for refraction

An interesting thing happens when light is going from a material with higher index to lower index, e.g. water-to-air or glass-to-air…there is an angle at which the light will not pass into the other material and will be reflected at the surface.

Using Snell’s law:

n 'sinθ ' = nsinθ

sinθc = nn'

sin90o = nn'

Examples:

Water−to−air

θc =sin−1 11.33

⎛⎝⎜

⎞⎠⎟=48.6°

Glass−to−air

θc =sin−1 11.52

⎛⎝⎜

⎞⎠⎟=41.1°


Total internal reflection

At angles > critical angle, light undergoes total internal reflection

It is common in laser experiments to use “roof-top” prisms at 90° reflectors.(Note:surfaces are typically antireflection coated)


Water−to−air

θB =tan−1 1.331

⎛⎝⎜

⎞⎠⎟=53.1°

Glass−to−air

θB =tan−1 1.521

⎛⎝⎜

⎞⎠⎟=56.6°

Examples:

θ + ′θ =90o

nsinθ = n 'sin ′θ = n 'sin(90o −θ ) = n 'cosθ

∴ θB = arctann '

n⎛⎝⎜

⎞⎠⎟

Brewster’s Angle


Fresnel Reflection Equations

Rs (θ) =sin( ′θ −θ)sin( ′θ +θ)

⎡

⎣⎢

⎤

⎦⎥

2

=ncosθ − ′n cos ′θncosθ + ′n cos ′θ

⎡⎣⎢

⎤⎦⎥

2

Rp(θ) =tan( ′θ −θ)tan( ′θ +θ)

⎡

⎣⎢

⎤

⎦⎥

2

=ncos ′θ − ′n cosθncos ′θ + ′n cosθ

⎡⎣⎢

⎤⎦⎥

2

R =n− ′nn+ ′n

⎛⎝⎜

⎞⎠⎟

2Examples: Air-to-water : R=2.0%Air-to-glass : R=4.2%

Polarization dependent Reflection fraction vs. incident angle

Normal incidence

Augustin-Jean Fresnel1788-1827


Fresnel Reflection

Air-to-salt salt-to-air

Salt: AgCl (near-IR)


Brewster’s: HeNe laser cell

TIR: Diamond cutting

Familiar Examples of Brewster and TIR

Want to MINIMIZE reflection here

Round trip gain must exceed round trip reflection losses to achieve laser output

Want to MAXIMIZE reflection here

Brilliant diamond cut must maximize light return through the top.


α

θ1 ′θ1

α

β γ′θ2

θ2

δ

′nn

sinθ1

sin ′θ1

=′n

n=

sinθ2

sin ′θ2

δ =θ1 +θ2 −α

Prism refraction


Second issue: Optical dispersion


Spectral Irradiance Monitor SIM

• Measure 2 absolute solar irradiance spectra per day

• Wide spectral coverage– 200-2400 nm

• High measurement accuracy– Goal of 0.1% (1)

• High measurement precision– SNR 500 @ 300 nm – SNR 20000 @ 800 nm

• High wavelength precision– 1.3 m knowledge in the focal

plane– (or < 150 ppm)

• In-flight re-calibration– Prism transmission calibration– Duty cycling 2 independent

spectrometers


SIM Prism in Littrow

2θ = sin−1 sinγn'

⎛⎝⎜

⎞⎠⎟+ sin−1 sin(γ −φ)

n'⎛⎝⎜

⎞⎠⎟

n’

Al coatedBack surface


SIM Optical Image Quality


SIM Measures the Full Solar Spectrum


d ≈t⋅n−1

nFor small angles:

Optical displacements “Careful!”


Focal length (thin lens)


Chromatic Aberration


Focal ratio (f/#)


Focal ratio con’t


Optical Transmission


Reflection or Refraction?


Reflection


Beam 2 travels a greater distance than beam 1 by

(CD - AB)

For constructive interference

m = (CD-AB)

m is an integer called the diffraction order

CD = dsinα & AB = -dsinβ

m = d(sinα + sinβ)

Note: sign convention is “minus” when diffracted beam is on opposite side of gratingnormal than incidence beam; “plus” when on same side

Diffraction grating fundamentals


Diffraction gratings use the interference pattern from a large number of equally spaced parallel grooves to disperse light by wavelength.

Light with wavelength that is incident on a grating with angle a is diffracted into a discrete number of angles βm that obey the grating equation: m. = d.(sin(α)+sin(βm)). In the special case that m=0, a grating acts like a plane mirror and β=-α

Blue (400 nm) and red (650 nm) light are dispersed into orders m=0,±1, and ±2

Diffraction grating fundamentals


Illuminate a grating with a blaze density of 1450 /mm With collimated white light and a incidence angle of 48°, What are the ’s appearing at diffraction angles of +20°, +10°, 0° and -10°?

d =1mm1450

x 106 nmmm

= 689.7 nm

=689.7nm

nsin 48° + sin 20°( ) =

748.4

nnm

β n=1 n=2 n=3

20 748 374 249

10 632 316 211

0 513 256 171

-10 393 196 131

Wavelength (nm)

Grating example


Plane waves, incident on the grating, are diffracted into zero and first order

650 nm

400 nm

Zero order

Reflection Grating Geometry

Rotating the grating causes the diffraction angle to change

α

€

λ=d•(sin(α)+sin(β))

Gratings work best in collimated light and auxiliary optical elements are required to make a complete instrument


Lenses are often used as elements to collimate and reimage light in a diffraction grating spectrometer.

Auxiliary Optical Elements for Gratings

Imaging geometry for a concave mirror. Tilted mirrors:1. Produce collimated light when p=f (q=infinity).2. Focus collimated light to a spot with q=f (p=infinity).


Entrance Slit

Exit Slit

Detector

Grating spectrometer using two concave mirrors to collimate and focus the spectrum

Only light that leaves the grating at the correct angle will pass through the exit slit. Tuning the grating through a small angle counter clockwise will block the red light and allow the blue light to reach the detector.

Typical Plane Grating Monochromator Design


Resolving Power

Na spectral lines

Na D-linesD1=589.6 nmD2=589.0 nmInstrument & Detector


For a given set of incidence and diffraction angles, the grating equation is satisfied for a different wavelength for each integral diffraction order m. Thus light of several wavelengths (each in a different order) will be diffracted along the same direction: light of wavelength λ in order m is diffracted along the same direction as light of wavelength λ/2 in order 2m, etc.

The range of wavelengths in a given spectral order for which superposition of light from adjacent orders does not occur is called the free spectral range Fλ.

1 + Δλ =m +1

m λ1

Free spectral range


The resolving power R of a grating is a measure of its ability to separate adjacent spectral lines of average wavelength λ. It is usually expressed as the dimensionless quantity

R =

=mN

Here ∆λ is the limit of resolution, the difference in wavelength between two lines of equal intensity that can be distinguished (that is, the peaks of two wavelengths λ1 and λ2 for which the separation |λ1 - λ2| < ∆λ will be ambiguous).

Resolving Power


SOLSTICE: Channel Assembly

‘A’ Channel During Preliminary Alignment Test


SOLSTICE: Channel Assembly


Solstice Instrument

The SOLar-STellar Irradiance Comparison Experiment consists of two identical channels mounted to the SORCE Instrument Module on orthogonal axes. They each measure solar and stellar spectral irradiances in the 115 - 320 nm wavelength range.

SOLSTICE B

SOLSTICE A

SOLSTICE Channels on the IM

Single SOLSTICE Channel - Dimensions: 88 x 40 x 19 cm - Mass: 18 kg - Electrical Interface: GCI Box


SOLSTICE Grating Spectrometer

• SOLSTICE cleanly resolves the Mg II h & k lines


Optical Aberrations


Spherical Aberration


Coma


Astigmatism


Optical Aberrations


Unwanted & Scattered Light


Cassegrain Baffling Example


The End Game


Optical Detection


“What’s the Frequency--Albert?”


Photomultiplier Tube Detectors

-1200 VGround

Output pulse

•A photon enters the window and ejects an electron from the photocathode (photoelectric effect)•The single photoelectron is accelerated through a 1200 volt potential down series of 10 dynodes (120 volts/dynode) producing a 106 electron pulse.•The electron pulse is amplified and detected in a pulse-amplifier-discriminator circuit.•Solstice uses two PMT’s in each channel that are optimized for a specified wavelength range

–CsTe (‘F’) Detector Photocathode) 170-320 nm

–CsI (‘G’) Detector Photocathode) 115-180 nm

Single photon detection (pulse counting) with an PMT


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