Limits to sharpness:

diffraction and seeing

Rich KronYAAYS

18 September 2007

tie-ins with YAAYS July/August camps:

✹making a telescope

✹scale model of Solar System

✹“F” box optics lab

✹(pinhole camera, rainbow)

telescopes are tools for focusing light

aside from that, they have three purposes:

✹see bigger (magnification)✹see fainter (light-collecting aperture)✹see sharper (resolution)

how telescopes work: demos

1) hold 2 lenses

2) project onto screen

3) how a single lens works

4) how a magnifier works

5) how refraction works

6) telescope as “super camera”

Christiaan Huygens’s summary of attempts to decipher appearance of Saturn (1659)

A

angle A is the angular size of Mars

Marsyou(on Earth)

A

Marsyou(on Earth)

angle A can be characterized by the ratio h/d

h

d

(measure h and d in the same units)

when Earth laps Mars, d is about 48 million miles

the diameter of Mars (h) is about 4200 miles

what is the angular size of Mars?

A = h / d = 4200 / 48 million = 1 / 12,000

to appreciate how small, we can construct a scale model: how far away does a penny need to be placed so that is has the same apparent size as Mars does?

hpenny = 3/4 inch

dpenny = 3/4 inch × 12,000 = 240 yards

dpenny = 240 yards

if a telescope is used to observe Mars with a magnification of (say) 100 × , then the penny seems to be 2.4 yards away

(this is roughly the same as the apparent size of the Moon with no magnification)

it still looks small!

Christiaan Huygens 1659Syrtis Major

image quality:

how do we quantify how sharp an image is?

what factors contribute to image blur?

what contributes to image blur?

✹ imperfect optics

✹ out-of-focus

✹ shake during exposure

✹ large pixels or too much data compression

what contributes to image blur (continued)?

✹ diffraction (bending of light around a sharp edge)

⇒ the image quality delivered by the Hubble Space Telescope is limited by diffraction

⇒ the image quality of ground-based telescopes smaller than about 5 inches is limited by diffraction

point ⇒Airy disk

larger aperture

⇒smaller Airy disk

spikes around stars are caused by diffraction of light around the support vanes of the secondary mirror

here, the Airy disks are too small to show

what contributes to image blur (continued)?

✹ atmospheric seeing (non-uniform refraction)

⇒ the image quality of the Yerkes refractor is limited by seeing

time series of short-exposure images of a star to illustrate seeing (W. Keel)

Q: I am limited by diffraction. What can I do?

A: 1) get a bigger telescope 2) observe shorter wavelengths (bluer light)

Q: I am limited by seeing. What can I do?

A: 1) get into space 2) use adaptive optics 3) pick a site with good seeing 4) try lucky-shot imaging

resolution test: fine dark lines on a bright background

Andrew Ellicott Douglass

Edgar Rice Burroughs

A Princess of Mars 1912

Chesley Bonestell, illustrator

1897

Giovanni Schiaparelli

grand niece Elsa

Camille Flammarion

Vatican Advanced Technology Telescope, Mt. Graham, AZ

1909

E. E. Barnard

Lick Observatory, CA

Alfred Russel Wallace“Is Mars Habitable?” 1907

daytime temperature of martian surface = - 50 F

Lowell’s legacy

Mars is covered with surface features that are likely (former) water courses

Mars may have significant amounts of water (but not liquid on the surface)

Mars may indeed be a good place to search for life (also Europa)

Pluto

Lowell Observatory, Flagstaff, AZ (research by Slipher, Douglass, Tombaugh, et al. continues today)

Summary

telescopes enhance our ability to see small details on distant objects

but, there are fundamental limits to how sharp we can see:

diffraction is important when the aperture is small

atmospheric seeing is important on the ground

what we see as “real” includes a complex interaction of physiological and psychological elements