From rmillan@ataman.harvard.edu Fri Jul 14 15:28:22 2000 Date: Fri, 14 Jul 2000 15:28:19 -0400 (EDT) To: brewer@fcrao1.astro.umass.edu Subject: Re: IOTA detectors From: rmillan@cfa.harvard.edu Cc: smorel@cfa.harvard.edu Mime-Version: 1.0 Content-Transfer-Encoding: 7bit Content-MD5: GTR7vjq6RVwn26llcNl5Aw== Hi Mike, This is a long answer to your question, but it allowed me to gather some basic numbers. -- Rafael. > Are you saying the current ISA bus I/O board is too slow? With the current ISA bus IO, the speed of data sampling using the current and planned systems is as follows. A clocking signal can be generated that has a max frequency of 300 KHz, or a period of 3.3 us. Half a period is 3.3/2 = 1.7 us. * A series of 7 IO operations is needed to setup: setup = 7 x 1.7 = 12 us * Row addressing is on rising edges: skip_row = 3.3 us * Column addressing is on both edges: skip_col = 1.7 us * ADC sampling time is 10 us NICMOS output settling time is 15 us Total sampling time is therefore: sampling = 10+15 = 25 us Let's assume in what follows that the target pixels will be located around the current optical axis point (row,col) = (32,32) of one quadrant. I will also assume that the target pixels will in all cases be located on row = 32. I also maintain the constraint that the target pixels be on even cols. The min. frame times below correspond to acquiring one data point for each target pixel, sampling each pixel once. They are calculated by grouping the terms as: (setup + skip_rows + skip_cols + sampling) (1) Current System (as a check) ============== This is classical beam combination with 2 telescopes and therefore 2 target pixels. Let's say the target pixels are on cols = 30, 34 Then the min. frame time is: 12 + 32x3.3 + 34x1.7 + 2x25 = 225 us = 0.22 ms (~ agrees with 0.18 ms measured) (2) Classical combiner, 3 telescopes ================================ The currently favored design is "all in one" (ref. I. Porro, W. Traub), where there will be 4 outputs, each containing 3 interferograms. They need to be separated in frequency by modulating the OPDs at different rates. Let's say the 4 target pixels are in cols = 28, 30, 32, 34 Then the min. frame time is: 12 + 32x3.3 + 24x1.7 + 4x25 = 275 us = 0.27 ms There are 2 moving piezos and 1 fixed piezo. If the 2 moving piezos scan at a speed such that the OPDs are modulated at speeds V, 2V and 3V, then there will be 3 peaks in the power spectrum at frequencies f/3, 2f/3 and f respectively. Assuming 3 data points per fringe, the max. fringe frequency will be: f_max = 1/(3x0.27 ms) = 1234 Hz The other 2 interferograms will be oversampled by factors of 3/2 = 1.5 and 3 and their fringe peaks will be at the max. frequencies: 2x1234/3 = 823 Hz and 1234/3 = 411 Hz The min. times to go through each packet of, say, 10 fringes will be: 8 ms, 12 ms and 24 ms; which are all below the nominal near-IR atmospheric coherence time tau_o = 50 ms. (3) Integrated Optics combiner, 3 telescopes ======================================== The currently favored design is "pair-wise" (ref. J-P. Berger), and there are 7 outputs, 4 photometric and 3 interferometric. The 3 interferometric outputs contain only one fringe each, corresponding to a single pair of telescopes. Therefore, although the 3 fringe frequencies will still be different (at most two will be equal), there is no longer the constraint that the fringe powers have to be well separated in frequency, and I will ignore this constraint here. Let's say the 7 target pixels are in cols = 26, 28, 30, 32, 34, 36, 38 Then the min. frame time is: 12 + 32x3.3 + 38x1.7 + 7x25 = 357 us = 0.36 ms Assuming 3 points per fringe, the max. fringe frequency is: 1/(3x0.36 ms) = 926 Hz And to record one packet of 10 fringes will take 11 ms, smaller than the nominal tau_o. Note that in all cases, for fainter sources, which require integration times per data point greater than the minimum considered above (which in practice we achieve by sampling multiple times at the above speeds and averaging), the fringe freqs. and time/packet will scale accordingly, with negative impact on our ability to detect the packets inside one atmospheric coherence time, particularly under bad seeing conditions. This however is irrelevant to the question of IO speed: fainter sources do require longer integrations to be detected, and one has to live with whatever the atmosphere does to the fringe signal. Conclusion ========== The current ISA bus IO board will be able to satisfy the minimum requirements of all the planned beam combining systems. The time budget is, for cases (1), (2) and (3) respectively: t_skipping = 175 us, 175 us, 182 us t_sampling = 50 us, 100 us, 175 us Therefore, at best equal amounts of time are spent skipping and sampling. Faster IO would translate in the capability to skip faster, which would significantly reduce the min. frame time. The benefit would be the ability to scan through the fringe packet faster, and reduce differential piston noise on bright sources. To each of the above min. frame time corresponds a "limiting magnitude": the faintest star that can be observed with the shortest integration time. For stars brighter than this limit, we can either welcome the extra photons, or reduce the integration time in order to scan faster. One could argue that to the extent that we decided that the numbers above adequately take care of the atmosphere under most conditions, there is no big premium in scanning faster, i.e. in using faster IO. A detailed answer however requires a calculation of SNR of visibility amplitude and phase which includes the effects of both decreased signal and piston noise with decreased integration time.