Imaging Brightness Variation 130mm Triplet APO f7 or f6.5

[roughy]

Whilst there are quite a few tools to calculate the difference in FoV, is there a formula to calculate the percentage difference in brightness between these to focal ratios?
Sensors that will be used are KAF8300 (5.4 microns) and MN34230 (3.8 microns).
Thanks
Mark

[gregbradley]

https://phlearn.com/magazine/f-stops-everything-you-need-to-know/

F7.1 to F5 is double the amount of light.

So F7 to F6.5 then is around 23%. I don't know the scale is linear though it may not be.

Theoretically with the same camera it should need around 20% less exposure time for the same brightness image.

Greg.

[mura_gadi]

Hello,

The total brightness of an object is determined from aperture only, and the f ratio only affecting the magnification when used with eyepieces/lenses.

So, with a given eyepiece used the shorter F ratio will magnify higher and cause the object to be bigger but dimmer. (Same light spread out over a larger area). If you could set the 130 to have the same magnification at f7 and f6.5 you should see no difference in brightness.



Steve
Ps. Sorry was referring to f ratio and not f-stops for lens aperture.

[The_bluester]

For your purposes, Greg is on the money, using a camera the faster ratio will be brighter.

But I would bet you that you will have a hard time measuring a meaningful difference between F7 and F6.5 for the same exposure and gain. I would bet the difference you will see from shot to shot is likely to be more than the difference that F7 to F6.5 will produce.

[gregbradley]

Yes the camera reference applies because the aperture does vary when you open up the aperture of a camera lens.

But practically speaking with regards to telescopes with a fixed aperture, if you add a reducer you will reduce exposure times and get a wider view. Hence the popularity of 8-12 inch scope with fast F ratio like F4 or less.
More of the light from the scene is allowed onto the sensor and when you have a long focal length its the same as cropping the field of view.

So the extra light is coming from the wider field of view.

The faster the F ratio the more difficult it is to have the image aberration free and the more sensitive to collimation etc.

Greg.

[JA]

Hi Mark,

Yes, it has to do with the way the f-Number is defined and the increase in light per unit area/field, but by way of a worked example:

in your question of an f/7 vs f/6.5 optic, the f/6.5 would be ~16% brighter.

(7/6.5)^2 = 1.15978

In other words the f/6.5 optic is 1.15978 times (~16%) brighter than the the f/7 optic.

Or if you prefer,
if the f/7 brightness were 100 units, then the f/6.5 brightness would be 115.978 units or ~ 16% brighter.

Best
JA

Also note that if the image circle differs between the 2 optics the considerations are more complicated, especially if there is any vignetting.

[roughy]

Thank you for all the input gents. Much appreciated.