Lin

Back to Psych 221 Projects 2013

Background

Original photon calculator utility suggestion

Build a program, perhaps based on the ISET library, that calculates the spectral irradiance at the sensor from the scene radiance and a specification of the optics. Doing this for diffraction-limited optics, specifying only the f/#, is sufficient.

The utility should be backed by a wiki page that illustrates all of the steps in doing that calculation. This project should produce an educational and useful calculator.

• Doing an implementation that can run on a browser on the Internet is best.
• Doing a straight Matlab implementation with a nice GUI is also good.
• Implementing the ISET (Matlab) routines as a Python calculator has value, as well.

Submitted project background

The program will (hopefully) run in a browser, be able to take in lens transmission as a function of wavelength (or be able to choose from presets of lenses, such as that of the human eye, thin lens glass, and camera lenses, though I can only find data for a Nikon 55mm as of now), and an f/# and lens magnification / distances. 

The calculation will also take into account cosine-fourth fall-off and irradiance blurring from diffraction. The program will get scene radiance from the two sample image scenes from ISET, and if possible, I'd like to make more scene radiance files (but it sounds like that requires special equipment) and lens transmission data (also, more special equipment, like a spectroradiometric measurer). 

An article with graphics describing the calculations will be made. 

Evolving project goals

An early draft of the project was completed and brought in to Professor Wandell for suggestions.

Original Photon Calculator

I also was interested in asking Professor Wandell how ISET/VSET was able to produce scene radiance from simple jpg files. The project in that state used VSET in order to calculate scene radiance from a jpg and an illuminant, and would then continue on to calculate irradiance incident on a sensor using the irradiance formula

$E={\frac {\pi }{1+4(f\#)^{2}(1+\left|m\right|)^{2}}}TL$

And furthermore apply cos-4th fall off / vignetting calculations of

$E_{off-axis}=E_{on-axis}\cos ^{4}\phi$

The plan was also to work on an algorithm for spatial blurring (assuming operation is diffraction-limited) of

$OTF={\begin{cases}{\frac {2}{\pi }}\left[\arccos(\rho )-(\rho {\sqrt {(}}1-\rho ^{2}))\right]&{\mbox{for }}\rho \leq 1\\0&{\mbox{for }}\rho \geq 1\end{cases}}$

And then to implement the VSET radiance calculations purely into Java, so the web application would be fully self-sufficient (i.e. not need VSET).

You can use subsections if you like. Below is an example of a retinotopic map. Or, to be precise, below will be an example of a retinotopic map once the image is uploaded. To add an image, simply put text like this inside double brackets 'MyFile.jpg | My figure caption'. When you save this text and click on the link, the wiki will ask you for the figure.

Below is another example of a reinotopic map in a different subject.
Figure 2

Once you upload the images, they look like this. Note that you can control many features of the images, like whether to show a thumbnail, and the display resolution.

Figure 3

MNI space

MNI is an abbreviation for Montreal Neurological Institute.

Methods

Measuring retinotopic maps

Retinotopic maps were obtained in 5 subjects using Population Receptive Field mapping methods Dumoulin and Wandell (2008). These data were collected for another research project in the Wandell lab. We re-analyzed the data for this project, as described below.

MR Analysis

The MR data was analyzed using mrVista software tools.

Results - What you found

Retinotopic models in group-averaged data on the MNI template brain

Some text. Some analysis. Some figures. Maybe some equations.

Equations

If you want to use equations, you can use the same formats that are use on wikipedia.
See wikimedia help on formulas for help.
This example of equation use is copied and pasted from wikipedia's article on the DFT.

The sequence of N complex numbers x₀, ..., x_N−1 is transformed into the sequence of N complex numbers X₀, ..., X_N−1 by the DFT according to the formula:

$X_{k}=\sum _{n=0}^{N-1}x_{n}e^{-{\frac {2\pi i}{N}}kn}\quad \quad k=0,\dots ,N-1$

where i is the imaginary unit and $e^{\frac {2\pi i}{N}}$ is a primitive N'th root of unity. (This expression can also be written in terms of a DFT matrix; when scaled appropriately it becomes a unitary matrix and the X_k can thus be viewed as coefficients of x in an orthonormal basis.)

The transform is sometimes denoted by the symbol ${\mathcal {F}}$, as in $\mathbf {X} ={\mathcal {F}}\left\{\mathbf {x} \right\}$ or ${\mathcal {F}}\left(\mathbf {x} \right)$ or ${\mathcal {F}}\mathbf {x}$.

The inverse discrete Fourier transform (IDFT) is given by

$x_{n}={\frac {1}{N}}\sum _{k=0}^{N-1}X_{k}e^{{\frac {2\pi i}{N}}kn}\quad \quad n=0,\dots ,N-1.$

Limitations

• The server controls (and shares) one Matlab session among all current users. There are solutions (using HttpSession in Java for example), but implementation requires some thought.

Conclusions

Here is where you say what your results mean.

References - Resources and related work

References

Software

Appendix I - Code and Data

Code

My code is hosted on GitHub, as per Professor Wandell's suggestions (minus vset, which should be in the starting directory and announced in Matlab with isetPath()).

Data

zip file with filter data and some simple Matlab scripts; should go in Matlab starting directory