Oleg Zabluda's blog
Friday, June 08, 2012

ISS star trail images from Don Pettit. 10-15 min exposure. Awesome!
ISS star trail images from Don Pettit. 10-15 min exposure. Awesome!

http://www.flickr.com/photos/nasa_jsc_photo/sets/72157629726792248/with/7257866592/
http://www.flickr.com/photos/69074860@N04/7197237418

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Let's calculate and sanity-check Hubble/KH-11 resolution and stuff.
Let's calculate and sanity-check Hubble/KH-11 resolution and stuff.

A plane wave, say from a point source at infinity, viewed through a a circular aperture creates diffraction pattern called Airy disk. When 2 such points are close together, their Airy disks overlap. People disagree what counts as "points are resolved", and it's different for camera vs human eye, and eye-to-eye. But it's on the order of θ = C * λ/D, where for astronomy, C is somewhere in between 1.220 (Raleigh limit 25% MTF), and 1.011 (Dawes limit, 5% MTF), and 0.61 ( Sparrow limit 0% MTF). For terrestrial observations, people often take 50% MTF, for which I estimate C=2, since I am too lazy to type Bessel functions into Wolfram Alpha.

Violet light is 380nm. 2*380e-9/2.4=3.2e-7 radians or 0.06 arcsec. Red light is 750nm, for resolution of 2*750e-9/2.4=6.25e-7 radians or 0.12 arcsec. KH-11 may or may not be shooting in ultraviolet and/or infrared. In red light, from 250km high, 250,000*6.2e-7=0.15m.

Let's compare it to me, as a spy satellite. When standing up, and looking down on the ground [1] (comparisons to Hubble/KH-11 are in parenthesis), my aperture is ~2.4mm (1000x), and altitude is ~2.5m (100,000). So my resolution is ~100x smaller, or 0.15cm. Which is exactly right (just checked).

For illustration, see Hubble's image of Betelgeuse, which is 0.05 arcsec:
http://imgsrc.hubblesite.org/hu/db/images/hs-1996-04-a-print.jpg

It also checks nicely with current crop of private Earth imaging satellites, which sell 1.0-0.5 m resolution images with mirrors 0.5-1.0 m. I even worked briefly for one, which shall remain unnamed until the info is public.  ﻿

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html
http://www.rocketmime.com/astronomy/Telescope/ResolvingPower.html
http://en.wikipedia.org/wiki/Diffraction-limited_system
http://en.wikipedia.org/wiki/Angular_resolution
http://en.wikipedia.org/wiki/Dawes_limit
http://en.wikipedia.org/wiki/Sparrow%27s_resolution_limit
http://www.normankoren.com/Tutorials/MTF.html

[1] In non-equatorial geosynchronous orbit, no less.
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/raylei.html

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Жечь было наслаждением.
Жечь было наслаждением. [...] Медный наконечник брандспойта зажат в кулаках, громадный питон изрыгает на мир ядовитую струю керосина ...
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It was a pleasure to burn. [...] With the brass nozzle in his fists, with this great python spitting its venomous kerosene ...

This always comes as a big surprise to ex-Soviet people, just as it did to us. We learned it only ~10 years ago, after we lived in US for ~10 years. To this day it seems to be very arcane knowledge (very hard to find online), since everybody assumes he wrote it either as anti-fascist (who burned the books very publicly in 1933), or anti-soviet (who did so privately, but, unlike fascists, together with their authors and readers), similar to Orwell's anti-soviet "Animal Farm" (1945) or "1984" (1949).

The Soviets translated and published F451 it in 1956, in an extreme example of double-think. By the time I was reading it in mid-80's, I was sure it was extreme samizdat anti-Soviet propaganda.

Bradbury never went to college, was self-taught in public libraries (just like Joseph Brodsky), was leftist in political views, seemed to know almost nothing about USSR at the time, and, as far as I can tell, didn't want to find out, and simply didn't care.

He was writing about what was surrounding him, and what he knew. How Americans, instead of reading books, were watching TV and Facebook. Books abridged (Cliff Notes) and modified to accommodate offended prudes, women and minorities, until the remaining garbage could just as well be burned [1].

It's a great social commentary, but he wrote many better books.

http://en.wikipedia.org/wiki/Book_censorship_in_the_United_States
http://en.wikipedia.org/wiki/List_of_most_commonly_challenged_books_in_the_U.S.

http://en.wikipedia.org/wiki/Fahrenheit_451