Consider a CCD with a quantum efficiency of 80 percent and a photographic plate with a quantum efficiency of 1 percent. If an exposure time of 1 hour is required to photograph a celestial object with a given telescope, how much observing time would be saved by substituting a CCD for the photographic plate?

CCD (Charge-Coupled Device) imaging is a technique widely used in astronomy to capture high-quality images of celestial objects. CCDs are highly sensitive electronic detectors that convert incoming photons into electron charges. This makes them far more efficient than traditional photographic plates, especially when dealing with faint astronomical phenomena.
The key benefits of CCD imaging include:

• High sensitivity and low noise, which enable the detection of faint objects.


• Greater linearity, allowing for more accurate photometry.


• Ability to store and process images digitally.
• Longer operational lifespan in observatories.

In the given exercise, a CCD with a quantum efficiency (QE) of 80% is much more efficient than a photographic plate with a QE of just 1%. This difference in quantum efficiency means that CCDs can make previously time-consuming observations much quicker and more precise.

Calculating the exposure time is crucial for capturing a clear image of a celestial object. Exposure time depends on the sensitivity of the imaging device and the brightness of the object. In this exercise, we are given:

• A CCD with 80% quantum efficiency.


• A photographic plate with 1% quantum efficiency.


• An original exposure time of 1 hour using the photographic plate.

The factor of improvement (FoI) can be found using the formula: \[ \text{FoI} = \frac{\text{QEC}}{\text{QEP}} \] where QEC is the quantum efficiency of the CCD (0.8), and QEP is the quantum efficiency of the photographic plate (0.01). Thus, the improvement factor is 80.
To compute the new exposure time with the CCD, divide the original time by the FoI: \[ \text{Exposure Time (CCD)} = \frac{1 \text{ hour}}{80} = 0.0125 \text{ hours} = 0.75 \text{ minutes} \] This significant reduction shows the efficiency of CCDs in astronomical imaging.

Efficiency improvement in astronomy is a major focus, as it can greatly enhance the capability to collect data from celestial objects. Here, efficiency is linked directly to the quantum efficiency of the imaging devices.
In our exercise, by switching from a photographic plate to a CCD, the overall efficiency of observing time significantly increases. This is because:

• High quantum efficiency means more photons are detected.


• Less exposure time is required to capture the same amount of detail.


• Equipment can be better utilized, leading to more frequent observations.

Specifically, the observing time saved can be calculated by subtracting the new CCD exposure time from the original photographic plate exposure time:

\[ \text{Time Saved} = 1 \text{ hour} - 0.0125 \text{ hours} = 0.9875 \text{ hours} \]
Converting this to minutes:
\[ 0.9875 \text{ hours} \times 60 \text{ minutes/hour} = 59.25 \text{ minutes} \] This means 59.25 minutes are saved, highlighting the drastic efficiency improvement.