You guys have been asking for more information
on crop factor, how focal reducers work,
and what implications they have
on macro reproduction ratios and video framing
on cameras like the Blackmagic Pocket 4K
and now 6K. Well, I think I've come up with a way
to explain all of those concepts at the same time
using an illustration in Photoshop, a chart in Excel,
and some macro images of my ruler.
Let's get Undone.
[offbeat music]
♪ Gerald Undone ♪
He's crazy.
What's happening everybody? I'm Gerald undone
and we're taking the Hobbits to Isengard,
but before that. I want to show you some illustrations I made
so I have a video coming out soon comparing
different focal reducers and speed boosters.
And one of the ways that I was testing them was to film
some macro 1:1 reproduction of my ruler and see how consistent
the field of view was across those different reducers.
This gave me an idea for a great way to illustrate crop factor,
the function of speed boosters, and what happens
to a macro lens on a crop sensor.
Now, I should specify that these results refer to when
you use a full frame lens on a smaller sensor as that's
generally the only time that you would use a speed booster.
Because as I've explained in previous videos crop lenses
work a little differently in that the optics
actually produce a smaller image circle
instead of a larger image circle being cropped.
But anyway, let's start with a full frame sensor looking
at a ruler at 1:1 And a 1:1 reproduction ratio, by the way,
in case you don't know, means that your macro lens
can reproduce an object the exact same size
on your sensor as it exists in real life.
We can prove this with a ruler because
we know that a full frame sensor is 36mm across
so our ruler when captured at 1:1 should only show
36mm of the ruler across the width of the frame.
That would be 1:1. 36mm on the ruler
for 36mm on the sensor. By the way, if you're a big fan
of how macro video looks but don't really have
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OK, now that we see what our ruler looks like
on full frame at 1:1.
Let's recreate that in Photoshop so that we can
use it for our demonstration.
OK. So here I have sort of
a re-creation of it in Photoshop
and the blue circle is going to be our image circle
and the ruler is still the ruler here and this is basically
what the camera is capturing and it's creating this image,
and this is what's being projected on our sensor.
And if we make the yellow box here
our full frame sensor, then it makes sense.
It's 36mm across and 24mm tall
and this is a 3:2 ratio,
but this is basically how it would work with projecting
the image onto the sensor at 1:1 reproduction of that ruler.
This isn't a measurement of the sensor.
This is the ruler being projected onto our sensor
For this one we're using 3:2 ratio because
that's what the sensor is but moving forward
we're going to use a 16x9 ratio, which is going
to come into the math a little bit later on.
So let's shrink this down to 20.25
which is the appropriate height for a 16x9.
Window of the sensor instead of 3x2
'cause it's going to be easier to work with 16x9.
OK, So now what would happen if we looked at this exact same
subject but through a smaller sensor like the Pocket 6K.
Well, it would look like this but you guys
already know all this. The classic boxes
in boxes explanation of crop factor.
The only difference here is that I've shifted the box
to the upper corner so that we can keep the measurements
congruent where normally the box would be in the centre.
We just continually crop into the centre of the image.
This also explains what happens with macro reproduction.
The lens is still reproducing the ruler at 1:1.
But our smaller sensor is only capturing a smaller portion
of it or around 23mm of the ruler, which also happens
to be the width of the Pocket 6K sensor, 23mm.
And this is where people start to suggest that macro
is actually more magnified on cropped bodies.
and it is and it isn't.
It is more magnified in the sense that we're seeing
a more zoomed in portion of the ruler than we saw
on full frame, but it isn't technically more magnified
because the ruler is still being reproduced
on a 1:1 ratio, as in that it takes up the same amount
of millimetres in real life as it does on the sensor,
in this case 23 when cropped,
so it's still a 1:1 reproduction.
We're just only seeing a smaller cropped portion of it
which gives us the illusion that we're seeing it more close-up
and that's essentially what crop factor is
in a nutshell. And if we looked at this
through the Pocket 4K, it would be even smaller
but still representing a 1:1 reproduction
of the sensor at 18.99mm.
Now when crop factor is conveyed, it's usually as
a multiplier, like 2x or in the case of the two sensors
we just discussed, it would be 1.56x and 1.9x respectively,
but I want to talk for a minute
about how that number is calculated and hopefully
settle a debate about the two different ways to go about it.
So over in Excel here I have
a very confusing looking document
but let me walk you through it.
So each one of these clusters
is just some simple math for a sensor
and it's actually really, really simple.
This one over here says full frame 3x2,
which as we just discussed in the Photoshop document
that's the full dimensions of the sensor
which are 36mm x 24mm.
Now, this next section is just some quick math to
do Pythagorean theorem to figure out the diagonal.
So I just squared this one, 36 becomes 1296
I squared 24, becomes 576. Add these two numbers
together you get 1872 and then find the square root
of those and you get 43.3.
So this is the diagonal measurement
of a 3x2 full frame sensor,
but like we did with the Photoshop document we have
to shrink that down to a 16x9 aspect ratio.
Which is what you see over here,
it becomes a 36x20.25
and the diagonal measurement now becomes 41.3.
This is the same all the way through it's going to be
you know width, height, diagonal for each one
of these blocks. Now, we can use this information to figure out
the crop factor of the Pocket 6K which is right here
and the Pocket 6K is 23.1mm across and 12.99mm tall
and the diagonal of that is 26.5mm. Now the two ways
you can go about it is you can either take the width,
36mm of the larger sensor,
and divide the width of the smaller sensor, 23.1,
and you will get a number, in this case 1.558, or 1.56x.
That's your crop factor 1.56x. But you can also
take the diagonal measurement, which is 41.3, and divide that
by the diagonal measurement of the smaller sensor
and you'll get 1.558. Now, they're extremely similar.
This one is 55 and this one's 44
but rounding wise it's going to equate to the same
and the difference is actually from earlier rounding
of the different numbers throughout this calculation.
What you'll see online a lot is people debating
whether you should go about it using
the diagonal method or the width method
and it really doesn't make a difference.
The only time it does make a difference is if you forget
to compensate for the aspect ratio,
so what'll happen is somebody will say, "Well I took
the 43 over here for the 3:2 full frame sensor and divided it
by this," which we can just do that really quickly here
and they'll get a number like 1.63
and they'll say, "Your crop factor is wrong.
It's actually 1.63." and some would say,
"No it's 1.56 because they did it this way."
If you compensate for aspect ratio correctly,
which would mean turn your full frame into a 16x9.
You can see that both produce exactly
the same number when rounded to you know,
the nearest hundredth. And over here
we have something similar, but this is
for the Pocket 4K. Now, the Pocket 4K
has sort of a weird aspect ratio. It's like 1.896:1.
So we have to do the same thing to our full frame sensor.
We have to turn it into a similar aspect ratio.
So in this case, it's going to be a 36mmx18.99mm sensor.
Basically, we're just-- we keep trimming off
the bottom of the sensor and the diagonal for that is 40.7mm
and the Pocket 4K here, these are the actual measurements,
it's 18.96 across by 10 tall and that gives us
a 21.43mm diagonal.
Again, the same thing, we can take the 36mm width
and divide it by the 18.96mm width
of the Pocket 4K and we'll get a one point...
1.9x crop factor, or we could do the diagonal
of the corrected aspect ratio full frame
and divide it by the diagonal of the Pocket 4K.
And again, we'll get a 1.9x crop factor
and you can use that crop factor in the other direction as well.
So say that you knew that the full frame is obviously 36mm.
And when we took the macro images of a ruler
it was 36mm across the frame. We could actually
just take that number and divide it by the crop factor.
In the case of the 6K, that would be 1.56x
and that'll tell us what we should expect to see
in our image if we're using a 1.56x crop factor.
And in that case it would be about 23mm.
And if we look at our actual macro footage
of the Pocket 6K you can see
that only 23mm is visible in the frame.
So that proves itself. Alright.
Now, let's add our last factor,
which is the focal reducer.
I use a speed booster on the Pocket 4K
and this obviously changes things but I feel like people
get confused about how to apply the previous calculation
to their crop factor and speed booster combination.
But again, it's just another example of two ways
to get the same result. In a previous video
I explained that speed boosters basically just focus
the image circle into a smaller more concentrated one
but now let's recreate that in our Photoshop diagram.
So if we imagine this blue circle and ruler
as our image circle like we talked about before
then what we need to do now is shrink it down
by the multiplier that's written on our focal reducer
in the case of the Metabones Speed Booster 0.71x
that I'm using to film this right now,
that means that we need to make our image circle
71% of the size that it is now.
So in Photoshop that's easy to do we'll just make a copy
of this but I'm only going to select the image circle
and the ruler and I'm going to transform those down to 71%
but I'm not going to change the size
of our coloured squares because those squares represent
our sensors and our sensors aren't physically changing size
just because our image circle is being reduced.
So now we can see that our image circle is too small
for our full frame sensor, which is true to real life,
and also that our Pocket 4K sensor is taking up
more of the ruler than it was before.
Now, it's coming in between 25 and 26mm,
and this can be seen in a real world macro video as well,
which was done on the Pocket 4K with the 0.71x Speed Booster
and the Canon 100mm macro set to 1:1 reproduction ratio.
We can see that our actual image of the ruler is again
taking up between 25 and 26mm.
So now we need to answer our two questions from before.
How does this affect reproduction ratio?
And how do we calculate the crop factor?
Well, our reproduction ratio is basically
out the window now because our sensor is not 26mm wide
because like I said, it didn't change.
So our reproduction ratio is now more like 1:1.4 instead of 1:1
meaning that every 1.4mm in the real world
is being represented as 1mm on our sensor.
And that's because the focal reducer squeezed
that 36mm image to be smaller than the lens reproduced it.
And the width we're seeing should be very close
to the 36mm width of the full frame sensor times the 0.71x
reduction of the focal reducer
bringing it down to 25.56mm.
Secondly, our crop factor is different now too,
we still have a 1.9x crop factor against a full frame sensor.
But we don't have a full frame image circle anymore.
We have 71% of a full frame image circle.
So there's two ways you can go about getting your new crop factor.
You can take your existing crop factor of 1.9x
and multiply it by the focal reducers factor of 0.71x
giving you 1.35x which would be your new boosted crop factor,
or you can take your full frame image of 36mm
and reduce it by the factor of your focal reducer
like 71% in our case, just like we did
in the Photoshop document and that will give you your new
image circle of 25.56mm and then you can divide that
by the width of the sensor that you're putting it on,
which is 18.96 in the case of the Pocket 4K
25.56 divided by 18.96 is again 1.35x.
People like to call each other stupid in the forums
for the different approaches to this math.
But as you can see, if you compensate
for aspect ratio, the result ends up the same.
The boosted crop factor is 1.35x
regardless of whether you reduce first and then crop it
or crop it and then divide it based on that.
Alright, so that's it. I don't want to add much more
as I feel we've said enough numbers for one video.
But if this video was successful, you should have
a better understanding of how crop factor
applies to full frame lens, what focal reducers do,
and how it affects macro reproduction.
And for those that are completely new to macro.
Hopefully you learned a little something
about reproduction ratios, and why having 1:1 on your lens
is important, and now when you read in the forums
people arguing about the difference between
diagonal crop factor and horizontal,
you can smile, knowing that if they compensated
for aspect ratio, they would get the same result anyway.
I also want to give a couple quick thank yous
to the groups that made this video possible.
Again, thank you to Storyblocks for sponsoring this video.
And also thank you to Camera Canada for lending me
the Canon 100mm Macro that I used for the tests.
And lastly, thanks to Adorama for lending me the Pocket 6K.
I've really been enjoying that camera so far
and I'll definitely have some more videos
coming out on it soon. Links to all that stuff
will be in the description down below.
But that's going to be it for me. I hope you found
this video helpful or at least entertaining
and if you did make sure you leave it the old thumbs up
and consider subscribing if you haven't already,
but if you did not find this video helpful or entertaining
feel free to hit the dislike button twice.
All right, I'm done.