Other than the difference in the quality of the image (increased focal length will produce more quality than the equivalent cropping of the image), is there a difference? For example, if I
increase focal length and don't crop
vs.
not increasing focal length and cropping image to be same size/view.
I am asking if there is a difference, distortion-wise, like when increasing focal length and backing up. Or will the images be the same other than quality? Particularly concerned with portraits.
From an idealized perspective, cropping and enlarging is functionally identical to zooming. In reality, of course, you lose pixels, and you probably lose real resolution as well since you are demanding more from the lens and camera system by looking more closely. Since you are discarding the edges of the frame, optical flaws — including lens distortions will be changed, often for the better.
But, you specifically ask:
I am asking if there is a difference, distortion-wise, like when increasing focal length and backing up.
which indicates that you are talking about perspective distortion. Perspective is affected by exactly and only one thing: where you stand. See What is the difference between perspective distortion and barrel or pincushion distortion? for more, or one of What does it really mean that telephoto lenses "flatten" scenes? or What's the succinct reason for face-warping in wide angle lenses?.
So: standing in the same place and cropping from a wide lens or zooming to the same framing will give exactly the same perspective. And, backing up and cropping or zooming to match will give the same perspective — but a new one from your earlier position. If you stand in the same place, there is no way to change perspective by either zooming or cropping.
I think the difference in quality due to cropping is not the real issue here. I think the differences encountered in the portrait setup are moot compared to the real issue which is facial distortion.
The camera doesn’t perceive things exactly the same as the human visual experience. That being the case, we must hone our skills to make portraits with the camera that please our clients. The portrait subject has a preconceived notion regarding their self-image. This is their view of themselves as seen in the dressing mirror. As a general rule, our task is to duplicate that view. If you succeed, you will have satisfied clients.
We are talking about “perspective”. Things close to the camera reproduce large and things further from the camera reproduce small. If the camera is positioned too close to the subject, the nose reproduces too large and the ears too small. The remedy is simply step back. Increased distance, camera to subject is the key. As we step back, the ratio of the distance between camera and nose and camera to ears diminishes. In other words, as we step back, we minimize facial distortion.
Stepping back is easier said than done. Sometimes the studio (workplace) is too tiny to allow the necessary increase as to subject distance. Thus we are forced to work in close, and this distorts facial features. Sometimes we use a lens with too short a focal length. When we do, the natural tendency is to compose by filling the frame in the viewfinder. If we just would step back, everything would be OK, but we abhor the empty space around the principal subject, so we stay put. The results are aggravated facial distortions.
Medium telephoto to the rescue: If we mount a moderate telephoto, we are forced to step back. This action is the ticket. The question becomes, “what is a moderate telephoto”? Over the years, portrait photographers gravitate to a focal length that is about 2X thru 2.5X longer than “normal”. So the questions become what is the “normal” focal length for my camera? The accepted normal for the FX (full frame) is 50mm. Thus the portrait focal length range is 100mm thru 125. For the DX (compact digital) “normal” is 30mm. Thus for the DX, the portrait range is 60mm thru 80mm.
We are talking rule of thumb; art has no norms so you are free to follow your heart. As to what is “normal” for the camera lens. The industry views “normal” as a focal length about equal to the corner to corner (diagonal) measure of the film or digital format. You will need to check your camera’s specifications to find the dimensions of the frame. As an example, the FX measures 24mm wide by 36mm long, the diagonal measures about 44mm. The DX measures 16mm wide by 24mm long, the diagonal measure is 30mm. If we mount a “normal” focal length lens, the angle of view is about 45° with the camera held horizontal (landscape).
Either would be the same view, which simplest (small) viewing may not perceive much difference. But yes, longer focal length gives more pixels that cropping would remove. So in that way (future potential of using the image for larger things), yes, longer focal length gives better image quality.
Maybe our camera takes 24 megapixel images, for example.
Double focal length would give for example, the same 24 megapixels, of the tighter view.
But using half the focal length, and then cropping 24 megapixels to retain half width and half height, to show as same view as the 2x lens, is only 6 megapixels. That is NOT the same quality. It's not a matter of distortion. It is that fewer pixels can only show less detail.
But if the smaller cropped image is sufficient pixels for the planned use, then there won't be much difference.
