Processing HI cube - I

Computing the orientation of each cell w.r.t. the central pixel

We would like to keep the simulation cube at a distance d (element: X=0, YMAX/2, ZMAX/2 is at a distance d).

Now, we compute angle subtended by all cells, and compute differential rotation velocity as per Brand and Blitz (1991).



1) Read velocity cubes Vxx,Vyy,Vzz

a) Compute projects of components of V_rot (due to galactic rotation) along the los.
b) Compute projection of velocities Vxx, Vyy & Vzz along the line of sight (los)
c) V_los = V_rot + components from step a


Formulae

a)
tan(theta) = y / (d+x)
(D * D) = (d+x)^2 + (y*y)

R' = sqrt ( D^2 + R^2 + 2*R*D* cos(theta+L)

Compute V(R') using Brand & Blitz (1991)

R" = D sin(theta + L)
phi = 90 - (theta+L)
phi" = arccos(R"/R)

V_rot = V(R') * cos(90 - (phi+phi") ) = V(R') * cos(theta + L - phi)

b)
theta = arctan(y / (d+x) )
V"yy = Vyy cos(theta)
V"xx = Vxx sin(theta)

chi = arctan(z/ (d+x) )
V"zz = Vzz cos(chi)

c) v_los (x,y,z) = V"xx + V"yy + V"zz + V_rot

Fractals and image characterisation

Some links are in order

1. Fractal Dimension: Wikipedia
   
2. A course on Fractals in Yale U
3. A course on Fractal dimension from images: Munich U
4. Fractal Dimension explained
   

So, once you know about fractal dimensions, come to read the stuff on the right (Conti, 2001)


One can treat the image 3-D object. Compute the total number of occupied boxes in X-Y-I dimension box, as a function of size of the box. D = ln(number)/ ln(radius).

It is a little bit more complicated. Check the paper by Conci, a PPT talk can also be found.

How to distinguish between landscape and portrait pictures?

1. Perhaps we can search for a large number of pixels with same natural colors: green, blue and black (shadows). look if a large fraction of pixels contain the same 'Hue' and 'Saturation'.
2. Another try: Look at the Fourier spectra of images, and mark radii of 60%, 90%, 99%, 99.9% power. they should be distinct for landscape images and facial portraits or nearby objects.
   
3. Human objects have a lot more symmetry than the natural objects. In fact, there could be some fractal pattern seen over the different length scales of an image of a natural scenery. Try to capture 'fractal' properties of pixels.

speaking of the last one: one could look at fractal dimension of a picture pixel values. How? Perhaps in the next blog post...

PHY GC 471 : Astrophysics, a first course

Course Description

This is a first course in astronomy aimed at a wide section of audience. We will introduce concepts with minimal use of mathematical tools. We would like to give a broad perspective of science to students, from regular night-sky astronomy to fascinating space astronomy. We will discuss historical context of some ideas and how they have evolved today. Keeping the engineering background of student population in mind, we will also emphasize on techniques, some challenging instrumentation, and details of space exploration.

Scope and Objectives

This being a first course to a variety of students from engineering background, we prefer to teach fundamental ideas about astronomy, and defer a detailed astrophysical treatment to another higher-level course. Astronomers study properties of light emitted by various sources in the sky. We will start by studying concepts of brightness, flux measurement and spectral-line observations, followed by instruments used these measurements. We will then discuss various astronomical objects, starting from our solar system, stars, to galaxies. In each case, we discuss basic astrophysical mechanisms to understand nature of light emitted by objects under consideration. We then discuss how to estimate physical parameters of stars, galaxies and the cosmos from the properties of light detected in various wavebands.

Textbook

IGNOU study material PHE-15 (Astronomy and Astrophysics), Indira Gandhi National Open University, 2006.

Astronomy Discussion Meetings: Proposal to the Astronomical Society of India

Over the past few years astronomy meetings have not been held regularly in India. Astronomical Society of India (ASI) only organizes bi-annual meetings, which are woefully short on discussions. To increase their frequency, topical discussion meetings involving a small number of active participants were proposed. Such meetings will allow a close interactions between astronomers, mainly from India. They will have an added benefit of smaller number of participants and of being focussed on topics of LOC's interests. The costs and local organization efforts will also be reduced significantly.

The ASI has accepted the proposal in principle. Here are the basic tentacles of such meetings. The ASI has granted a sum of 1 Lakh towards expenses of the meeting. One could further approach DST/ISRO/UGC for more funding. Given Ranjan being in DST committee, it would be easier from them.

There will typically be sessions over 2 and half days, with about 15 presentations. The emphasis is on discussions. Hence, followed by one 45 minute talk, there is 15 minute's break for Q/A session. At the end of each session, there will be an hour of open debate on possible new work, or comments on on-going work. This is place for on-board calculations, and some laptop demos, etc.

The meeting crucially depends on 4/5 resource persons. These will chair sessions, seed discussions and direct the course of the meeting. Their participation is vital, as is the willingness of the public to discuss issues and settle them on the spot, rather than defering to person-to-person discussion.

There will be about 10-15 faculty and 10-15 PhD scholars. Most members will stay during the entire two and half days of the meeting. There are no frills, except perhaps one institute buffet and some drinks from the LOC. The number is restricted to a number of 25, and is by invitation only. Most participants will not be provided travel support, and the local travel support will be provided on pay-per-use basis.


All these are thought to make the arrangement work of the LOC minimal, allowing for more groups from India to host meetings. This will allow a larger number of meetings, wider set of meetings, and dispersing meeting venues.


Amen to that!

Stop Sexual Harrassment

The title says it all...

Data Acquisition Block Diagram

The data acquisition of a band-limited signal has the following broad steps:

1. DC removal



2. 2-bit ADC (0.5 MHz speed)




Collect 4 such samples at one time (for simplicity, copy the same signals 4 times)




3. Build a sampler, of 0.5 MHz.




One could take 10 MHz signal, and use every 20th pulse (simple counter) for sampling.




4. Put together four 2-bit samples on a bus with an isolator for i/o.



5. Feed the signal to the data acquisition card sitting in the PCI slot of a PC.

BITS Goa Radio Telescope : Software Correlator

Thanks to Aniket and Mandar, we will get a data acquisition card interfaced to a PC by next semester.

All the card does, is to accept AC voltages of 250 KHz bandwidth, digitize it (2-bit ADC) and sample it at Nyquist rate (500 KHz). Four samples (2x4 bits = 1 byte) are then packed together on the fly to form one byte. The resultant one-byte is stored on a PC for processing. So, the pipeline looks as below


--- signal ---- >>-- ADC -->>--Linux PC-->>- FILE
(0.5 V AC________3-level____bit packing
0.25 MHz band)___2-bit_________program


ADC has two comparators (NE 521 ?). Depending upon the input, one of the the following 00 (-2), 01 (-1), 10 (+1), 11 (+2) is the output of the ADC.

The sampler signal of 0.5 MHz samples the ADC output voltages. Four of the samples are fed to the acquisition card through data cables.

The data rates are slow, 500 k Bytes per second. Given the modern computer disk rates, it is possible to sustain a on-the-fly bit packing program in PC. The program accepts 4 bytes, and based on a precalculated table, stores corresponding 1-byte output onto a file.

LO and Sampler Frequency Solution

We have our RF band as 73 - 74.6 MHz. Using one of the frequencies given by the Oven Controlled Crystal Oscillator, we would like to generate LO (of) such (frequency) that, our band is folded at some suitable IF. The end of the IF band should be the sampler frequency, again one of those given by the oscillator.

The first image is one such combination for the RF band and LO (plotted very quickly using PLOT program in Mac).


Given the 0.26 MHz band ending at 4.096 MHz beyond LO (70 MHz), the IF band looks as given in the second figure. The IF band now falls between 0 MHz and 4.096 MHz, although mostly empty (0-3.75 MHz), due to our RF filter.

The band is now sampled with 8.192 MHz, the sub-harmonic of 16.384 MHz from the oscillator.

Since both LO and sampler frequency are derived from the same ref, there should be more stability in the system.

One can have another combination of such a LO and sampler frequencies. As an exercise, try these two frequencies and draw the plots: LO (76.8 MHz) and Sampler (5 MHz).

Using the Crystal Oscillator

Our Band is 73-74.6. How do we use a Oven Controlled Crystal Oscillator, referred in the earlier post? We need to generate an LO signal (between 70-80 MHz) to bring RF signal to an IF of 2-5 MHz. We also need to use one frequency for our sampler.

We have a few frequencies at our disposal, 10, 12.8, and 16.384 MHz, etc. We should use 10 MHz for sampling, after some downconversion (0.5 MHz for 0.25 MHz band). This would be easy, using a digital counter. How do we go about LO? we need one frequency such that a bandwidth of 0.25 MHz in the above band gets down converted at IF.

It depends upon a combination of IF, and bandwidth we choose. The problem is, if the band has a lot of interference, we should be able to switch to some other location nearby (within 73-74.6). A smaller bandwidth makes this possible, while bringing down data rates.

I have a couple of solutions, I will detail two in the next post.