Wilt wrote in post #18349116
As I stated earlier, " 'funnels' the light
in a somewhat collimated manner'
A grid or snoot does NO true collimation, it merely masks the beam so its angle of coverage is not as wide.
That we agree.
A collimated source creates a somewhat harsher shadow edge.
Dito. By collimated, I assume you mean what I called "parallel" in terms of light rays reflection.
Which isn't a collimated (parallel) light source at all
.
BTW, I hope that we are talking about a silver BD here, because it makes no sense to talk about "collimation" or "parabolic" with a white modifier as white scatters light in all direction regardless of the angle of the light rays that strike it.
, in being a somewhat large (compared to subject head) source which is used relatively close to the subject, has the harsher shadow of the collimated source yet also with some shadow penumbra softening of a larger source.
A result that can be obtained with any modifier that will give you the same light distribution when looking into the modifier from the subject's POV (in the case of Beauty dishes, often like the pictures above). That in itself is uncorrelated to whether the thing collimates light rays or not or the beam angle. If we were to put the subject in a room made of Ventablack, you wouldn't see any difference between various modifiers with various beam angles as long as they are illuminated in the same way from the subject's POV.
To illustrate the effect (and ignoring the tangent about mathematical profile of the beauty dish!) of a somewhat collimated source, one can look at page 49 of
Master Lighting Guide by Christopher Grey, 2004. (Unfortunately permission is needed to reproduce portions of this book electronically.)
You aren't seeing the effect of a collimated light with the pictures shown on p49. You are seeing the effect of the effective light source's size, from the subject's POV (which may be different from its physical size) and the light intensity evenness / distribution of that modifier's interior from the subject's POV.
To go back to your suggestion to the OP, i.e. to choose a parabolic umbrella made with the same material as the BD, and the same size, the thing is in reality quite a lot more complicated.
For example :
1) most pseudo parabolic silver umbrellas will look like this from the subject's POV. That's a fairly (actually, significantly) different pattern from all hard silver BDs and the shadows will definitely look quite different (multiple edges galore in general). I've seen only one pseudo parabolic silver umbrella that avoids this bicycle wheel illumination pattern, Paul Buff's soft silver PLM. That's because it uses a silver material that scatters light a little bit more than the usually more reflective silver materials that are used with most pseudo parabolic umbrellas (you could argue that it doesn't behave like a parabolic modifier then
). That's another problem : there are a lot of different silver materials with different light reflection properties.
HOSTED PHOTO
please log in to view hosted photos in full size.
2) Most white umbrellas can be used so that you get a rather narrow hotspot when looking into it, either by shoving the light source inside or choosing an appropriate reflector, which somewhat-ish corresponds to what a lot of white BDs do. But then it doesn't need to be parabolic as white materials scatter light rays in all directions anyway. Deep white umbrellas, which aren't parabolically shaped at all, can be used to that effect.
3) In both cases umbrellas will behave quite differently from most BDs in other areas (beam angle, mounting practicalities, etc...) - i.e. things aren't simple. In addition, finding the right umbrella with the right size may be difficult. There isn't a smaller soft silver PLM than 137cm for example these days.
4) If you expect something else from a BD other than just the "harsher shadow of the collimated source yet also with some shadow penumbra softening of a larger source" then a tremendous quantity of other factors come into play. What if I told you, for example, that what I personally use a white BD for, I replicate (and far from exactly) with an octabox with a modified front diffusion layer

?
So that's the problem : it's difficult to present CanonYouCan an alternative to a BD since BD designs and results vary widely, other modifiers designs vary widely, their uses vary widely, expectations vary widely.
It is, sometimes, easier to find alternatives. For example, a Paul Buff soft silver PLM with its front diffusion cover gives a somewhat similar light as a similarly sized typical octaboxes with several diffusion layers and without grids. Even then, many variables may make one choose one over the other. But beauty dishes ? Too many variables to be able to give a simple answer.