Saturday, January 27, 2007

A series of improbable events

1) Getting an interview from Toshiba despite the fact that my DOST debts will prevent me from going outside the Philippines.
2) Seeing Glenn of theory lab in MRT on his way home from Ayala (around 3pm).
3) Seeing my brother also on the same train cab for a Magallanes-Cubao trip with pet stuff from Cartimar Pasay, just in the side opposite Glenn's.
4) Wearing a lite colored formal attire.

Saturday, January 20, 2007

What is your wavelength?

"One small step for man, one giant leap for mankind."
--Neil Armstrong

"One small bug for programmer, one giant error for results."

After getting unexpected results from my c/c++ pseudo-generalized implementation of Richard's and Wolf's vector diffraction integral (Electromagnetic diffraction in optical systems II), I finally found out what causes the problem (although I still don't know exactly why).
With my work with a spatial light modulator (SLM), I consider that each square SLM pixel has a side of 2mm/768. Then I scale the wavelength to pixel units, so 1 wavelength = 0.02433846153846153846 pixels.

I tried it for different numerical apertures and topological charges. The numerical aperture had to be too small (.0001) before getting expected far field results. Usual values (0.1 order of magnitude) result in what looks like symmetric noisy data. But the results resemble that of Richards and Wolf's when I blow up the image to sub pixel dimensions, thus I thought it was just brought about by simplifications (neglecting the lens's phase contribution, putting the object field at the lens,etc...).

As it turns out, the wavelength assumed seems to be small with respect to the pixels. I learned from FDTD simulations that the discretization of space voxels should be at most 1/10 of the wavelength (1/20 recommended). This avoids the error caused by truncating higher order terms when numerically differentiating with Maxwell's equations. I didn't expect that to be the case for diffraction integrals too. Thus I set 1 wavelength = 20 pixels.

So far it works.

(a) (b)
(c) (d)

Figure 1. Calculated electric fields for an aperture radius of 32 in the center of a 128x128 computational array. Shown are the resulting image field intensities for different topological charges of the object field (1 for a and c, 0 for b and d) and numerical apertures of the lens (0.1 for a and b, 0.999 for c and d).
The modulus of the Ex Ey and Ez components are encoded to the Red Green and Blue channels respectively. It can be seen that the fields are predominantly linearly polarized along the x-axis for low NA values.

Friday, January 12, 2007

Those missing days

The familiar high pitched tune as a 56kbps modem dials a predefined set of numbers during the first few minutes of the day invokes a nostalgic feeling in me. Stranded in my residential habitat with nothing left from SPP and without the semester's stipends yet makes you realize how long 24 hours could be (psychological time dilation). With nothing to do but eat, sleep, and those mechanical, redundant house hold chores, Christmas vacation felt just like another alibi for not staying home.

A card stacking pattern made popular by Hunter X Hunter's Hisoka (SONY optical USB mouse in the background)

I realized that it was more difficult to make a "Hisoka card stack" with smaller cards (approx 2 x 3 cm2). I used to easily reach 3 to 5 stories with standard cards. With these miniature ones,I already gave up at 2. Inertia came into my mind, the smaller cards having less mass are less likely to stay in their position. Then came friction; with less surface to rub against the base, the cards would slide easier. Finally came the thought that if DOST was faithful in providing their scholar's stipends on time, I would have had a standard sized deck.

P is for Paper. A Guy Fawkes mask based on the rendition of David Lloyd

I thought that I would be adding some drawings to my collection during the break, but I decided to go 3d instead. Just expressing my artistic/autistic mind. It looked good with my naturally long hair back then.

I eventually realized how generic our book collection is, when I could not find any advanced geek physics or programming stuff to ponder with at home. Without a decent compiler I was forced to experiment with browser interpreted Javascript. I also had to endure the slow (about 3kbps) download speeds for Javascript and DOM e-books (with such a slow connection, I decided to disable loading images in firefox). I should have burned some e-books from the lab.

Oscillating some strings while RJ's broken guitar gently weeps.

But everything was not that bad after all. On December 22, I went to RJ's house before my last year's stay at the lab which lasted until December 23. Nothing had changed much after half a decade, he still is that friendly funny practical person I knew back in high school. He thought me how to solve a Rubik's cube with pictures (how to deal with the center pieces' orientations). He was also the one who thought me how to solve the cube with only a plain color on each face. Shamefully, all I can give for Christmas's sake was the vodka awarded to me for being the most intimidating IPL member application examiner (which I rarely thought of utilizing).

Clouds and sky over San Mateo. Looks so good, you'd think it's a wall paper.

Also, the December 30 San Mateo reunion with relatives on my mother's side was worth while since I rarely have a chance to swim. That is where I thankfully received some cash from the least expected uncle. Sometimes (in a year), it feels good to be with people who have similar genes as yours.

For those of you wondering if I had been dead during my absence else where (equivalently my presence else where else (compliment of impenetrability, "No thing could be at two places at the same time" "(cf No two things could occupy the same space at the same time)")) these are among the stuff that I had been doing. And I had my phone off most of the time (especially on peak seasons) to avoid those holiday spams (peace of mind).