Know your camera - sharpness versus f-stop

One of the important things to do when starting to shoot is to get to know your camera. Know it's strong points and it's weaknesses. Use the first, mask the latter. The camera I'm currently using is the Panasonic hc-x929 which is identical to the hc-x920. For reasons unknown to me the model number varies slightly depending on the region where it is sold but they are technically identical. It has essentially the same lens and sensor unit as the ag-ac90 model, so much of what I am going to say in this post about my camera will also directly apply to these models. I will explain the type of tests I perform to assess my camera's properties so you may repeat them with your own camera and I will ofcourse show my results for this particular camera. If your camera happens to be similar the results will propably also apply to your's.
One of the first things to asses is it's sharpness as a function of it's f-number. Every camera has a sweet spot in terms of it's f-number where the lens performs best. In short, when selecting a low f-number (i.e. a wide open aperture) you are using the entire lens surface to capture the light, both the center and the edges. Most lenses suffer from spherical aberration. Light passing through the edge of a lens is generally not focussed to the same spot as light passing through the center, causing a blurred image. When a high f-number is used (i.e. a small aperture) you are using only the center part of the lens elements but the narrow opening between the iris blades will lead to diffraction diffusion. If you don't take these effects into account when choosing your settings your images may show up somewhat blurry.
In photography, as a rule of thumb it is generally assumed the optimal f-number is 1.5 to 2 stops above it's lowest f-number. However with this camera you will find there is a twist to that rule-of-thumb which I will demonstrate further down. Let's first just describe the "test-procedure" used.
Select a test scene to shoot with some fine, high contrast detail in the center of the image. (The sides of the images may suffer from unsharpness or other distortions which are not directly related to the f-number.) A test chart from which you can read off the actuel sharpness as a number is nice but not realy necessary for this mere amateur. In the end we will not be shooting all our footage with just one f-stop setting anyway, it suffices to know in what range you roughly want your f-stop to be.
Put the camera on a tripod or a stable surface. Use manual exposure and shutter speed and leave all other settings at their default setting for now. Disable all image stabilizer functionality. It may use digital tricks or create artificial motion blur, both of which may throw off your measurements. Once the camera has obtained focus, switch to manual focus so you can be certain you don't get an out-of focus shot because the camera suddenly decided to refocus. You will want to shoot a scene with plenty of light so you can use both high shutter speeds with wide apertures (low f-number) and slow shutter speeds with small apertures (high f-numbers).

No Panasonic consumer camera's will allow you to first set an aperture and then select a shutter speed to get correct exposure. Instead you will have to do the reverse; first select a shutter speed and than set the aperture to get a correct exposure. So start with the slowest shutter speed i.e. 1/50 (or 1/60 if you're recording at 60 frames per second). Don't use any of the slower shutter speeds as these require your camera to perform digital tricks which may affect your sharpness. As soon as you set the shutter speed, the aperture will be controled automatically. Now the aperture can be switched to manual again and it's value will be displayed on the lcd screen. Adjust the exposure when required and make a recording. Note with each recording the f-number used. There should preferably be enough light to start your measurement with a stop of f11 or higher and the amount of light should be constant. With each recording the shutter speed can be increased a notch and the f-number will have to be decreased a notch to arrive at the same exposure, so by starting at f11 you can be certain you have covered the entire range of interest.
After having taken all shots you can upload them to your computer and examine them one by one. Now you should note that not all are equally sharp. Let's show a few samples I made, all blown up to 200 percent:

f1.5

f2.8

f4

f5.6

f9.6

Now I have to admit that when I recorded these shots I had one of the image parameters of the camera (confusingly called "sharpness") set to minus 5. Only later I discovered that this setting is sub-optimal, With the default setting of zero the differences between the shots would have been more pronounced but for the purpose of this test it fortunately did not matter much. Hey, I make mistakes and describe my findings so you don't have to make the same mistakes.
Notice how f2.8 is sharper then both f1.5 and f4? This corresponds to our rule of thumb that the sharpest f-stop is about 1,5 to 2 stops away from the smallest f-number. However, do you also notice how f5.6 is sharper then f4? In fact f5.6 appears to be as sharp as f2.8.
I made a whole series of shots at different f-numbers and if I were asked to roughly sketch the sharpness as a function of f-number I would come up with something like this:

Conclusion; for optimal sharpness one should try to pick an aperture near 2.8 or 5.6. Try to avoid f4 if sharpness is of crucial importance or any of the apertures at the extreme end of the range. Note that this applies specifically to the camera I use i.e. the x920/x929 and ac90 from Panasonic. Other camera's may behave differently or have different optimal aperture settings.

After this discovery I performed another experiment which allowed me to more clearly see what is going on. In the follow-up post I will explain what is causing this odd behaviour.