Thursday, February 11, 2010

The Rayleigh Criterion: The Bane of Mirrored Telescopes?

Named after a 19th Century English physicist, is the Rayleigh Criterion the true arbiter over press hype of the true capabilities of large mirrored telescopes and reconnaissance satellites?

By: Ringo Bones

I could have titled this blog entry as; “Is the KH-Series of American Reconnaissance Satellites’ Capability of Seeing Soviet-era Pravda headlines from 160 kilometers up Somewhat Overly Optimistic?” but that would only answer a part of a little understood concept of optics. And if the “hype” over the runaway success of adaptive optics were to be believed, would this imply that the best astronomical telescopes could soon be found here on Earth as opposed to orbital space? Though that too is only part of the story, but the point of this discussion is about how an oft-ignored, yet vital aspect, of advanced telescope design. Whether using a Hubble Space Telescope-sized 2.4-meter primary mirror or a 10-meter primary mirrored Earth-based astronomical telescope is ultimately diffraction limited. This means that the resolution of a large reflecting telescope – whether those on the KH-series reconnaissance satellites, the Hubble Space Telescope, or those very large astronomical telescopes found on top of Mauna Kea or in the Chilean desert – is limited by diffraction.

The first person to study the diffraction limitation problem of reflecting or mirrored astronomical – or other large - telescopes was a 19th Century English physicist / gentleman-scientist named John William Strutt, but he’s better known to the rest of the world as the 3rd Baron Rayleigh or Lord Rayleigh. Also more famous for his 1904 Nobel prize for Physics for the discovery of the element argon – which he isolated in cooperation with Sir William Ramsay – than his work / investigations in optics that lead to the criterion named after him. The Rayleigh Criterion defines the resolution capabilities of a reflecting telescope where two points are just resolved when their angular separation is equal to an angle designated as theta at which the first diffraction minimum occurs. As given in the equation theta = 1.22 multiplied by the wavelength of light of interest divided by the mirror diameter of the telescope. The number 1.22 is a constant derived by Lord Rayleigh when he used differential equations in tackling this problem. The angle theta can also be designated as dividing the linear separation of the characters of interest – like the headline of a Soviet-era Pravda newspaper at around an inch or 2.5 cm – with the orbital altitude of the reconnaissance satellite – often at 160 kilometers up.

If anyone – besides me – is really curious if a KH-11 like reconnaissance satellite is really capable of seeing clearly a Pravda newspaper headline from 160 kilometers from the Earth’s surface. One can use the Rayleigh Criterion to test to test whether the KH series of reconnaissance satellite’s capabilities are nothing more than cold War era media hype. Let’s just assume that the KH-11 reconnaissance satellite has a main mirror similar in size to that of the Hubble Space Telescope at 2.4 meters since the two are almost of similar dimensions. Assuming that it works in the visible light spectrum at 550 nanometers (smack down in the middle or the green portion of the visible light spectrum) as the wavelength of interest.

So to get the resolution limit of your typical reconnaissance satellite, just multiply 1.22 with the orbital altitude of the reconnaissance satellite – usually around 160 kilometers or 160,000 meters. Multiply this number with the quotient that resulted when the wavelength of interest – 550 nanometers (550 times 10 to the negative 9 meters) – is divided by the reconnaissance satellite’s main mirror diameter of 2.4 meters. The resulting figure is 4.47 centimeters, which makes the reflecting telescope of your typical reconnaissance satellite really have a hard time seeing a Pravda newspaper headline – even license plates – from 160 kilometers up. The letters and numbers may be 4.47 centimeters tall but if they are spaced closer than 4.47 centimeters, the resulting image will be a blur if taken from 160 kilometers up. Shifting to the longer infrared wavelengths worsen the resolution when looking at “small” objects, while the shorter ultraviolet wavelengths could face problems of increasing atmospheric opacity from going through more than 100 kilometers of air.

There might be truth to the rumors of the gripes of “civilian” optical technicians working on the Hubble Space Telescopes main mirror during the Reagan Administration being denied access to the mirror testing equipment primarily used to test the main mirrors on the KH-11 series of reconnaissance satellites. Citing national security concerns back when America was still engaged in a Cold War with the Soviet Union. Sadly, this resulted in the Hubble Space Telescope’s technicians not knowing that the telescope’s main mirror is ground a few millionths of an inch too much while still on the ground in the NASA clean room. Worse still, the astronomical community only knew of the Hubble’s misshapen mirror only after it has been launched 350 kilometers into orbital space when they tested it, hence the then famous press headline of the Hubble Space Telescope being a 1.2 billion dollar blunder.

Maybe, the end of the Cold War proved to be a blessing in disguise to the Hubble Space Telescope because there are rumors too that the potato chip-shaped “corrective lenses” that are retrofitted to the Hubble back in 1993 were borrowed from the KH series of reconnaissance satellites. Maybe this specially shaped lenses are the “magic wand” that allowed the NSA reconnaissance satellites to beat around the Rayleigh Criterion / diffraction limitations of space-based reflecting telescopes. Regardless whether they are used to look up and out into space or look down on Earth’s surface in search of WMDs.


VaneSSa said...

Those portable telescopes with 8-inch mirrors being pitched at amateur astronomers as the minimum required to see Pluto technically has a problem seeing the "Dwarf Planet" from Earth's surface when the Rayleigh Criterion is taken into account. Let me explain.
Pluto has a mean diameter of 5,800 kilometers and is 5,842,000,000 or almost 6 billion miles away from us. Using 550 nanometers (the mid range green-yellow portion of the optically visible part of the electromagnetic spectrum) as the wavelenth of interest. Using the Rayleigh Criterion, a telescope with an 8-inch or 0.2-meter diameter mirror has a resolution x = 19,539.91 kilometers. Given that Pluto is only about 5,800 kilometers across, Pluto will look like a featureless star through an 8-inch reflecting / mirrored telescopewhen seen from the Earth's surface.

May Anne said...

I wondered why Engineering Connections with Richard Hammond have not discussed the Rayleigh Criterion when the show explored the evolution of astronomical telescopes - or the polymath John William Strutt a.k.a. Lord Rayleigh? Have you considered the concept of Optical Interferometry to circumvent the limitations imposed by the Rayleigh Criterion on reflecting or mirrored telescopes? Tenured professional astronomers had been using this technique for sometime now. Harold A. McAlister of Georgia State University is an astronomer who frequently used the line : " If you built a stadium on the Moon, you couldn't even see it from the Earth's surface through the best optical telescopes." McAlister champion the use of Optical interferometry to go around the Rayleigh Criterion limitations of refracting / mirrored telescopes by using two or more widely separated telescopes to achieve the equivalent resolving power of a single astronomical reflecting telescope as large as the distance between the telescopes.

Yvette said...

Another way of circumventing the limitations imposed by the Rayleigh Criterion is though aperture synthesis. Sir Martin Ryle won the 1974 Nobel Prize for physics - the first ever awarded to an astronomer - for developing this method. Aperture synthesis was also adopted by the US DoD in the from of Synthetic Aperture Radar that eventually liberated Kuwait during Operation Desert Storm back in 1991.

Anne Lynne said...

Given my hazy memories of my advanced engineering mathematics classes in college, the factor 1.220 is derived from a calculation of the position of the first dark ring surrounding the central Airy disk (named after a 19th Century optical physicist bloke named Airy) of the Diffraction pattern. Factoring diffraction through a circular aperture, then the calculation involves a Bessel Function - where 1.220 is approximately the first zero of the Bessel Function of the first kind of order one. As in J sub 1 divided by pi - i.e. 3.141592654... This factor is used to approximate the ability of the human eye to distinguish two separate point-sources depending of the overlap of the Airy discs where the minimum of one point source is located at the maximum of the other. This is the reason why modern telescopes and microscopes - even reconnaissance satellites in loe Earth orbit - with video sensors (charge coupled devices) may be slightly better than the human eye in their ability to discern the overlap of Airy discs. Thus explains the ability of NSA spy satellites to read Soviet-era Pravda headlines and car license plates in downtown Moscow during the Reagan administration.