Title: Advancing Physics AS Teacher Edition
Author: The Institute of Physics
Last saved by: Authorised User
Company: Tasker Milward

Bits and bytes in images
Question 110S: Short Answer

Calculating and estimating amounts of information:
These questions are about calculating numbers of pixels, and amounts of information in bits or bytes.  Show all your working clearly.

Eyes and digital cameras
Although we are unaware of it, our eyes detect light in discrete areas, or picture elements (pixels), they are receptor cells on our retinas. These are the rod and cone cells, named for their physical shapes. 

Cone cells are about 1.5 μm across, and are mostly concentrated in the fovea, or yellow spot on the retina. Assume they are packed in square array and close contact, as in the diagram.

1.	Calculate the area occupied by each cell on the retina (treating it as a square)

2.	Calculate the cell density or number of cells per mm^2.

3.	Take the radius of your fovea as 2 mm. Use πr ^2 to find the number of cone cells ('pixels') in your fovea.

CCD cameras
First generation digital cameras using CCD sensors had about 320 × 240 pixels, on a 6.4 mm × 4.8 mm silicon chip.

4.	What is the length of the side of the pixel in such a camera? 

5.	Calculate the pixel number and density for the camera and compare to the human eye.

6. Such cameras usually operate on a 256 level brightness scale from 0 to 255 for the brightness of each pixel. This can be coded as a one byte binary number (8 bits).  How much information in bytes does a single image in this camera store? 

Photographs

Conventional photographic film contains silver halide crystals or grains, which are sensitive to light (a nucleating atom of silver which is later developed into a silver grain is produced by the arrival of about 10^-18J of light energy per crystal, independent of the crystal size). You can think of these grains as like 'pixels'.

A fast film for action shots (say Formula 1 racing) has a short exposure time (1 / 1000 s), so the grains are made relatively large to catch more light per grain. Even so the grains are typically 5 μm across, giving respectable but not very high resolution.  

For astronomical purposes, very slow film with many fine grains down to 20 nm in size is used. Resolution is much better, but exposure times are correspondingly longer. 

7.	How many times more 'pixels' are there in a slow film than a fast film of equal area?

8.	What minimum exposure time would you recommend for the slow film?

9.	Give some reasons why this is a minimum estimate.

Each grain will be exposed or not-exposed during the photographic development, so it has two states, binary 0 or 1, i.e. one bit of information is stored per grain. A photographic plate in the UK Schmidt sky survey telescope is about 360 mm × 360 mm. 

10.	How much information can one such slow photographic plate store? (You may assume that the plate is completely covered in grains.) Give your answer in bits and in bytes.

A large CCD
In 1998 the world's largest CCD was 4096 × 4096 pixels. The detector was smaller in size than a photographic plate, being 40 mm × 40 mm (limited by the size of current silicon wafer technology), hence having a smaller field of view.

By 2006, CCDs with 8 million pixels were readily available, and ones with 1 million pixels were common in mobile 'phones.

11.	4096 has a special significance in binary. How many bits are needed to count 4096 different states? (i.e. 2 raised to what power equals 4096?)

12.	How many pixels are there on this large CCD? How does this compare with what was available in 2006?

13.	What is the linear size of the square pixels?

14.	If the charge on each pixel can be read to a resolution of 10 bits (1 part in 1024), how much information in Mbytes is stored in one such CCD image?

Television

Colour television screens and computer monitors work by adding different intensities of the three primary colours red, blue and green from adjacent pixels.

Colour TVs work on 625 horizontal lines by about 1000 vertical elements.

Computer screens work on various graphics standards: VGA 640 × 480 colour pixels; SVGA 800 × 600 colour pixels or 1600 × 1200 colour pixels.

There are 3 pixels, one for each primary colour, making up one colour pixel. 

15.	For each of these formats find the total number of pixels, allowing for 3 colours in each position.

Each pixel requires a byte of information, and typical refresh rates are 25 frames per second for smooth moving picture quality.

16.	Find the maximum rate of information transfer for a full-screen video SVGA signal.

You should be able to see the need for high bandwidth transmission, fast processors and graphic compression routines.