# Interesting Telescope Image Recording and Transmission Design Problem! Need help!

## Homework Statement

You have been tasked with the design of a new far-field, high resolution imaging system to be placed on
the Hubble Space Telescope. This system will be used for taking deep space astronomical images with an
exposure adjustable between 10 minutes and 24 hours based on the brightness and distance of deep space
objects. At the end of every 24-hour period the Hubble Space Telescope will transmit the image data to
the ground station as it passes overhead. All image data prior to transmission is stored on a single 4.7
GB RAM disk in the Hubble telescope, and the telescope camera must bedesigned such that the
maximum storage capacity on board cannot exceed in any given 24 hour period.

a) If each pixel on the camera image sensor supports a maximum dynamic range of
4096 (dynamic range is equivalent to the number of levels of each color) for each of three color channels
(red, blue, and green), determine the maximum resolution (frame size) in pixels of a camera with a 4:3
ratio of horizontal and vertical pixels that can be supported on the Hubble Space Telescope.

b) The Hubble Space Telescope is in orbit 500 miles above the Earth's surface, and
makes one polar rotation around the earth per day. The telescope passes over the ground station once per
day, and needs to be within 700 miles to transmit data to the ground station. Estimate the data rate that
must be supported to offload all 4.7 GB of data to the ground station on each pass.

(Hint; The diameter of the Earth is 7,901 miles, and you can neglect any Earth rotational effects)

c) You decide to encode all of the data using a Hamming (15:11) code by breaking the
data stream into appropriate lengths, and increase the storage capacity of the RAM disk aboard the Hubble Space Telescope to compensate for the additional bits required by the Hamming code. Calculate the new storage capacity of the RAM disk required to support adding the Hamming code information to the data before storage.

d) Due to increased solar activity, the Hubble Space Telescope is now only able to
transmit when it's within 525 miles to the ground station. Estimate the new data rate that must be supported to offload ail of the dam to the ground station on each pass using the conditions of Part (c).

2. The attempt at a solution

frames per day = 144frames/day

number of bits to represent the color levels is log(base2)4096=12

so 12 bits per color, so in total 36 bits per pixel are required for color.

the ratio is 4:3 so we can consider the image pixels as 4x * 3x

(3x*4xpixels/frame)*(3colors/pix)*(12bits/color)*(144 frames/day) = ?

I am stuck here and have no clue what to do.

Mark44
Mentor

## Homework Statement

You have been tasked with the design of a new far-field, high resolution imaging system to be placed on
the Hubble Space Telescope. This system will be used for taking deep space astronomical images with an
exposure adjustable between 10 minutes and 24 hours based on the brightness and distance of deep space
objects. At the end of every 24-hour period the Hubble Space Telescope will transmit the image data to
the ground station as it passes overhead. All image data prior to transmission is stored on a single 4.7
GB RAM disk in the Hubble telescope, and the telescope camera must bedesigned such that the
maximum storage capacity on board cannot exceed in any given 24 hour period.

a) If each pixel on the camera image sensor supports a maximum dynamic range of
4096 (dynamic range is equivalent to the number of levels of each color) for each of three color channels
(red, blue, and green), determine the maximum resolution (frame size) in pixels of a camera with a 4:3
ratio of horizontal and vertical pixels that can be supported on the Hubble Space Telescope.

b) The Hubble Space Telescope is in orbit 500 miles above the Earth's surface, and
makes one polar rotation around the earth per day. The telescope passes over the ground station once per
day, and needs to be within 700 miles to transmit data to the ground station. Estimate the data rate that
must be supported to offload all 4.7 GB of data to the ground station on each pass.

(Hint; The diameter of the Earth is 7,901 miles, and you can neglect any Earth rotational effects)

c) You decide to encode all of the data using a Hamming (15:11) code by breaking the
data stream into appropriate lengths, and increase the storage capacity of the RAM disk aboard the Hubble Space Telescope to compensate for the additional bits required by the Hamming code. Calculate the new storage capacity of the RAM disk required to support adding the Hamming code information to the data before storage.

d) Due to increased solar activity, the Hubble Space Telescope is now only able to
transmit when it's within 525 miles to the ground station. Estimate the new data rate that must be supported to offload ail of the dam to the ground station on each pass using the conditions of Part (c).

2. The attempt at a solution

frames per day = 144frames/day

number of bits to represent the color levels is log(base2)4096=12

so 12 bits per color, so in total 36 bits per pixel are required for color.

the ratio is 4:3 so we can consider the image pixels as 4x * 3x

(3x*4xpixels/frame)*(3colors/pix)*(12bits/color)*(144 frames/day) = ?

I am stuck here and have no clue what to do.
This is actually a pretty good start. What you're not using is the fact that the transmissions have to fit on a 4.71 GB RAM disk. This would be 4.71 X 109 bytes, or 4.71 X 109 X 8 bits. This number should go on the right side of your equation above, so you can then solve for x, the number of pixels in one row of a frame.