Physics 681: Solar Physics and Instrumentation –

Lecture 6

Carsten Denker

NJIT Physics DepartmentCenter for Solar–Terrestrial

Research

September 20, 2005 Center for Solar-Terrestrial Research

Tools for Solar Observations Limitations

General difficulties Seeing: description and definition Seeing: How to live with it Adaptive Optics Image Restoration

High-Resolution Telescopes Spectrographs and spectrometers Filter and Monochromators Polarimetry Special-Purpose Instruments

September 20, 2005 Center for Solar-Terrestrial Research

Limitations The Sun is the only star, where we can resolve

surface details! Instrument Earth’s turbulent atmosphere Solar observations can be photon starved!

larger apertures, more efficient instruments, longer exposure times

Atmospheric extinction Space missions: Ulysses, Yohkoh, SoHO, TRACE,

RHESSI Ground-based projects: FASR, ATST, GREGOR,

and NST

September 20, 2005 Center for Solar-Terrestrial Research

Seeing Degradation of image quality: image motion, differential

image motion, and blurring Boundary layer seeing vs. high-altitude seeing (jet-stream) Site selection is critical Refractive index fluctuations (pressure equilibrium but

temperature fluctuations)

Thermal convection in the entire troposphere Correlation time scale ≈40 ms (day) and ≈160 ms (night)

short-exposure times spectroscopy becomes difficult Isoplanatic patch size ≈5–10 arcsec Spatial resolution under good seeing conditions ≈1 arcsec

Fried-parameter r0 ≈ 10 cm Adaptive optics and/or post-facto image reconstruction

4 0

0

/1 2.79 10

/

P Pn

T T

September 20, 2005 Center for Solar-Terrestrial Research

Point-Spread Function (PSF)

0, , PSF , ; ,I x y I x y d d

2

1

1PSF /D r J br r

1.22 / (Rayleigh criterion)D

September 20, 2005 Center for Solar-Terrestrial Research

Modulation Transfer Function

PSF , exp 2 x yS q x y i q x q y dxdy

1/ 22 20

0

MTF 2 PSF 2 with x yq r r J qr dr q q q

September 20, 2005 Center for Solar-Terrestrial Research

Spectral ratio:

Power spectrum:

Cross spectrum (Knox-Thompson):

Bispectrum:

2 2

2 2

i i

i i

F q S qq

F q S q

2

2

0 2

i

i

F qF q

S q

* * *0 0i i i iF q F q q F q F q q S q S q q

*i i iF q F p F q p

Image Reconstruction

September 20, 2005 Center for Solar-Terrestrial Research

Speckle Masking

September 20, 2005 Center for Solar-Terrestrial Research

Phase Diversity

September 20, 2005 Center for Solar-Terrestrial Research

Wiener Filter

ˆ /F D S F

ˆ / /F D S F N S

ˆ DF W

S

2

2 2d

d n

F S PW

P PF S N

SNR

SNR 1d

d n

PW

P P