Although the aperture size is the one constant throughout this process - the results often emulate gear that doesn't exist. If you're curious to know exactly what that is then this page might help...
Let’s say you take 9 shot (3×3), perfectly aligned and with 50% overlap. You will end up with an image that has exactly two times (2x) the dimensions in each axis (see diagram below). So, however much larger your stitched image is, compared to a single full frame image, is how much you divide your lenses values by, to reach your equivalent single image from a full frame lens.
So, if you had used a 100mm f/2.0 (@ f/2) to shoot the panorama then the resulting stitched image would be equivalent to a 50mm f/1.0, as long as you don't crop it. This is much easier to work out if you are shooting with a full frame camera, otherwise comparing it to a single frame from the same camera won't give you the correct equivalent.
Going back to the example from the First Page - Since the panorama has matched the focal length of the wider angle lens we can work out the equivalent f-stop by knowing how much larger the aperture is on the longer focal length. In this case it's exactly 3 times (75 ÷ 25 = 3), so we can divide 1.4 by 3, which = 0.4666666 (which I then rounded up to 0.47).
Camera Sensor Size
The panorama (above) can be calculate one of two ways:
a 35mm f/0.47 lens on a 24 x 36mm sensor
a 135mm f/1.8 lens on a 93 x 139mm sensor
The first example can also be worked out by dividing the lens values by how much larger the final stitch is compared to a single image. In this case - 3.86 times larger. 135 ÷ 3.86 = 35 for the focal length & 1.8 ÷ 3.86 = 0.47 for the f-stop. This also confirms the above calculation.
The alternative way to see equivalency is to view it as the sensor being the thing that grows. we still maintain the 75mm aperture here, but the image circle of the lens expands along with the sensor size. we use the same multiplication, but on the sensor size instead - times each dimension of the full frame (24 x 36mm) by 3.86, which = 93 x 139mm.
This means we have emulated a sensor size somewhere between Medium and Large Format, whilst retaining the 135mm f/1.8 lens characteristic, projected to the larger image circle. Just like the full frame equivalent 35mm f/0.47 lens - nothing like this exists because it would be too big, heavy and expensive to manufacture into a commercially viable product. A lens to shoot this image in a single click would make Sigma's 1.6Kg Bokeh Monster lens (105mm f/1.4) look like a cheap pancake lens.
Maximising The Effect
What makes this technique great is seeing a wide image with an extreme subject isolation. This works best when you're able to accurately visualise your final resulting stitch. This will likely involve you getting really close and taking tiny portions of your subject in each shot. If you shoot from a similar distance you're used to (from the longer lens) you'll end up with a lot of space around your subject and a rather lackluster effect. This will likely take a little practice if you haven't tried it before.
Working out what a panoramic stitches dept of field is equivalent to on a single full frame lens is fun. Generally it helps most of us get a feel of its capabilities, but this is an arbitrary value that will anger some to its usefulness. This can be done for any sensor size that isn't full frame. Taken to an extreme this can be done for small smartphone sensors to show their large depth of field (not shallow). To help illustrate this I made the following diagram.
This camera phone lens doesn't have a variable aperture, so it's stuck at f/2.2 all the time. However it's equivalent depth of field is on an f/17 lens. Everything on this page is in relative scale to each other (sensors, lens apertures, single images & panoramas.