What is a webcam? • Webcams are small digital video cameras that hook up to your computer at the USB or Firewire port • Some webcams are true CCD devices (like the Philips ToUcam) • The produce 320x240 pixel images (and other resolution modes as well) • They are lightweight & Cheap, $100 or so… • They produce color digital video files with sound (avi file format)
Many varieties of Webcams • Logitech QuickCam - one of the first to be used by amateur astronomers for Lunar and Planetary work. • Philips ToUcam has been a very popular and inexpensive webcam for astronomy and is the camera I use. • an excellent entry level webcam costing around $130. • There are higher performance (and much more expensive) webcams used by advanced amateurs for astronomical purposes (Luminera,DMK21F04, Point Grey). • DMK: $390 for the camera, $199 for filter wheel, $285 for filter set. • Lumenera: $995 for camera alone. • Point Grey Research has some nice fire-wire minis ~$700 or so • Avoid currently available CMOS devices, they lack sensitivity compared to CCD based devices. • Color vs gray-scale - filter wheels vs deBayering.
What’s Inside a typical webcam? Lens with NIR filter CCD chip behind window Microphone Video Circuit Board USB connector and cord
How do you use it for Astronomy?(you are going to void your warranty) 2) Add 1.25” adapter and NIR blocking filter 1) Remove lens and discard 3) 4) Replace eyepiece with the webcam Plug webcam into your laptop…
If you’re lucky and persistent, you will get some .avi video files of planets jiggling around with fleeting glimpses of details on the edge of visibility, a lot like what you see through the eyepiece. You can also extract single frame snapshots from the video, but they tend to be blurry and don’t show the detail you glimpse in the video. Wouldn’t it be great if we had some way to take the information that we know is in the video, and somehow put it all into one picture?
Well, thanks to a young Dutch amateur astronomer/computer programmer named Cor Berrevoets, we have a FREE downloadable program named REGISTAX which does just exactly that: http://registax.astronomy.net/html/v4_site.html • Here’s what Registax does: • Examines every frame of your video file • Does a critical evaluation of its quality. • Arranges frames in order of quality • Lets you pick a reference frame and how many of the best ones to keep. • Aligns each frame with the reference frame • Adds the frames digitally (stacking) • This gives an enormous improvement in signal to noise ratio (by √n). • Uses wavelet analysis to sharpen low contrast details in the image. Believe it or not. This image came from the video we saw in the previous slide! There are some details we need to deal with before we start getting pictures to rival the Hubble….
Critically Important Factor: Critical Details: • To get good results we need to match the resolution of the telescope to the digital sampling ability of the webcam • We do this by amplfying the focal length of the telescope until the smallest resolved image details are big enough to be realistically sampled by the pixels of the webcam CCD • We determine how much magnification we need using the digital sampling theorem - also the basis for high fidelity digital music recording and the operation of cell phones.
The Digital Sampling Theorem • In 1927 Harry Nyquist, an engineer at the Bell Telephone Laboratory determined the following principle of digital sampling: • When sampling a signal (e.g., converting from an analog signal to digital ),the sampling frequency must be at least twicethe highest frequency present in the input signal if you want to reconstruct the original perfectly from the sampled version. • His work was later expanded by Claude Shannon and led to modern information theory. • For this reason the theorem is now known as the Nyquist-Shannon Sampling Theorem
What does this all have to do with webcam astronomy? • The image made by the telescope optics is a two dimensional analog signal made up of spatial waveforms • A webcam is a digital sampling device Let’s re-state the sampling theorem in terms that relate to telescopic imaging using a webcam: • The sampling frequency implied by the pixel spacing on the webcam CCD must be at least twice the highest spatialfrequency present in the image to faithfully record the information in the image. If you violate this rule it’s called UNDERSAMPLING Undersampling is BAD…
Effects of Undersampling: Alias signals - illusions, not really there We can illustrate this with a digital scanner and a radiating line pattern: 60 dpi 13 dpi 302 dpi 23 dpi Oversampling is ok… Undersampling is not! How can we avoid undersampling in our imaging?
Here is a highly magnified view of a small portion of the surface of the webcam’s CCD: The maximum spacing of 15.8 microns on the diagonal determines the sampling frequency: ns = 1 sample/15.8 m = 1000 samples/15.8 mm = 63.28 samples/mm The Nyquist frequency is exactly one half this value: nN = ns/2 = 32 cycles/mm Default mode 2x2 binned, 320x240 This is the maximum spatial frequency the webcam can accurately sample in any telescope image.
Here’s how the pixels are utilized in the “higher” 640x480 resolution mode: The maximum spacing of 11.2 microns in green pixels determines the sampling frequency for green light: ns = 1 sample/11.2 m = 1000 samples/11.2 mm = 89.29 samples/mm The Nyquist frequency is exactly one half this value: nN = ns/2 640x480 mode No binning = 45 cycles/mm However, blue and red still have a Nyquist frequency of 32 cycles/mm
Here’s how the pixels are utilized in the 160x120 mode: Pixels are “binned” into 4x4 pixel arrays with vertical and horizontal spacings of 22.4 microns and a diagonal spacing of 31.6 microns. The minimum sampling frequency is: ns = 1 sample/31.6 m = 31.64 samples/mm The Nyquist frequency is: 4x4 binned 160x120 pixels nN = ns/2 = 16 cycles/mm
Now let’s talk about the resolution of the telescope. First, some optical definitions:Focal length = FAperture = D = diameter of lens or mirrorFocal ratio = F/D(usually written f/# as in f/8 or f/2.5 or referred to as f-number or f-stop) image D F
Spatial Frequencies in the Telescope Image Diffraction causes the image of a point source to be spread out into a circular spot called the Airy disk: d d • The diameter of the disk, d, is dependant only upon the focal ratio (f#) of the optical system and the wavelength, l, of the light used: d = 2.44lf# = 1.34f# • = 1.34*f# (for green light l=0.55m)
How do we convert this information into a spatial frequency? d/2 = 1.22lf# d/2 Two points of light separated by the radius of their Airy disks can just be perceived as two points. Raleigh Limit for Resolution
Minimum Spatial Wavelength Based on Raleigh Limit d/2 Imagine the images of many points of light lined up in a row, each separated from the next by the radius of their Airy disks: The sinusoidal wave resulting from adding all the images can be used to define the minimum spatial wavelengths present in the image lmin = d/2 The highest resolved spatial frequency, nmax = 1/ lmin = 2/d = 1/1.22lf#.
So, in the image from the telescope, we find that the maximum spatial frequency, nmax, is given by a simple formula: Maximum spatial frequency = nmax = 1/1.22lf# For green light, l = 0.00055mm At f/6, nmax = 248 cycles/mm At f/15, nmax = 100 cycles/mm Now that we know how to calculate this, we can “match” the maximum spatial frequency with the Nyquist frequency, nN , of our webcam. Setting nmax = nNand plugging it into the above formula, we have: nN= 1/1.22lf# , which rearranges to: f# = 1/1.22lnN = minimum focal ratio to avoid undersampling f# = 1/(1.22* 0.00055*32) = 46 This applies to both the 320x240 mode and for red and blue images in the 640x480 resolution mode.
An alternate expression for the maximum spatial frequency is given by the cutoff frequency where the MTF goes to zero contrast: Maximum spatial frequency = nmax = 1/lf# For green light, l = 0.00055mm At f/6, nmax = 303 cycles/mm At f/15, nmax = 121 cycles/mm Setting nmax = nNand plugging it into the above formula, we have: nN= 1/lf# , which rearrange to: f# = 1/lnN = minimum focal ratio to avoid undersampling f# = 1/(0.00055*32) = 57 Again, this applies to both the 320x240 mode and for red and blue images in the 640x480 resolution mode. However, one could argue that critical sampling at the cutoff frequency is silly, since there is no information available there.
Oversampling • Astronomers doing high resolution solar imaging routinely oversample by 50% • This seems to result in higher contrast, particularly at high spatial frequencies
How do we get the magnifications we need? • Barlow Lens or Powermate • Microscope Objective Transfer Lens • Eyepiece Projection
A Barlow Lens is a good way to achieve magnifications in the range of 2x to 3x and most amateurs already have one in their eyepiece box. It’s not a good idea to try to use a Barlow lens at a significantly higher power than its design magnification. Spherical aber-ation is introduced this way and can harm the image quality. Stacking of two Barlows to get 4x works better. Nagler sells Powermate image amplifiers that work well in this application although they are expensive. They are available in powers of 2x, 2.5x, 4x and 5x. They are used exactly like a Barlow lens.
Microscope objectives are a convenient way to gain high magnification with excellent optical quality. Typically, 5x, 10x, 20x and 40x are available. The 5x and 10x would be useful for this purpose. They are designed with a 160 mm back focal length, and the front working distance to the object being magnified is a little less than 160/M mm where M is the magnification. They are designed to work at the stated magnification (etched on the barrel of the lens) but can be used at slightly higher magnifications because we are not using their full numerical apertures with an f/6 beam.
The third easy way to couple a webcam to the telescope is using Eyepiece Projection. You need to make a short extension tube that fits and locks over the eye end of the eyepiece and which accepts the webcam adapter on the other end. A wide range of magnifications can be obtained by this method which has a long history of use for conventional astrophotography in the amateur community. Magnification achieved and the quality of the image obtained are dependant upon the power and quality of the eyepiece. Plössl eyepieces and orthoscopics should work well.
The atmosphere also affects the image: The effect of atmospheric turbulence is to blur and bounce around the perfect Airy disk image until it doesn’t look so pretty any more: } excellent good average poor bad V IV III II I Various qualitative seeing scales A quantitative measure of seeing is the Fried Parameter, r0. This parameter is expressed as a length and is the diameter of the largest telescope that would be diffraction limited under prevailing conditions. r0 varies less than 5 cm under poor seeing conditions up to values as high as 30 to 40 cm for excellent seeing at the best sites.
Here is the statistics for how r0 varied at one high altitude observatory site: Bad Poor Average Good Excellent 10 5 3 2 1 0.8 0.6 0.4 seconds arc.
According to Cavadore*, the probability of getting a good image from a single exposure is determined by the aperture size and the Fried Parameter, r0: By “good image” he means an exposure taken when the wavefront error across the aperture is no more than l/6.28 (0.16 waves). 1/P is the number of exposures you have to take to get a single good one. * Cyril Cavadore, Seeing and Turbulence, http://www.astrosurf.com/cavadore/optique/turbulence/
Here is how this probability affects our chances of getting usable images with the webcam: If we get lucky and seeing gets to be as good as average, the 12.5” will give one good image for every 100 frames that we take. To get 100 good frames, we need to take 10000 frames! Stop down when the seeing is unfavorable • In poor seeing conditions (what we have most of the time) it takes • About 20 frames to get one good image from a 5” aperture • More than 10,000 frames from a 12.5” aperture • Forget about it for a 24” aperture
Stopping Down Note that when you stop down a telescope because of bad seeing, you don’t need to use as much magnification to reach the critical sampling focal ratios. For example, our 24” Cassegrain telescope at Sperry has a focal ratio of f/11. If it were to be used at full aperture, 4 to 5x magnification would normally be needed to reach the f/45 or so needed to avoid undersampling with the webcam. Putting a 10 inch off axis stop on it changes the focal ratio to f/26 so we need only a 2x Barlow to achieve critical sampling and at the same time reduce the aperture to a more likely match to New Jersey’s seeing. Putting a 5 inch off axis stop on this telescope changes the focal ratio to f/44 without any amplification, just about right for critical sampling and a good match for poor to average seeing.
Length of Video Planetary rotation imposes a limit on how many frames you can take with your webcam. Emmanuele Sordini has figured this out for us at: bloomingstars.com Here are his recommendations for Mars, Jupiter and Saturn based on keeping image blur smaller than the resolution of the telescope and sampling ability of a webcam:
Noah My night assistant
10” f/17.6 Newtonian. Barlow lens mounted on-axis in front of small diagonal. Scope mounted on Losmandy G11 Germain Equatorial. Later installed in observatory. Used for Mars Opposition in 2003 and high resolution Jupiter pictures.
Moon image made with small refractor at f/6. Notice sampling artifacts.
Mosaic of Plato Region Taken with ToUcam coupled to 10” f/6 Newtonian with Barlow lens. EFL=176 Stopped down to 4” aperture, f/44
Saturn April. 2 2003, 2. 5x Barflow Lens 10” f/6 Newtonian Nov. 16 2004, 5x Powermate 12.5” f/6 Newtonian Jan. 22 2005, 5x Powermate 12.5” f/6 Newtonian Feb. 3 2006, 5x Powermate 12.5” f/6 Newtonian
Price tag of observatory: $4,000,000,000 $4000