Understanding the significance of the math

Rikke Rask
wrote:

boggis the cat
wrote:

Rikke Rask
wrote:

From 24x36 to 15.8x23.6 is about 1.2 stops.

From 15.8x23.6 to 13x17.3 is about 0.73 stops.

That's for "1.5x" APS-C.

That's for Nikon DX, yes. The best APS-C cameras available at the moment.

Are there
other
variants of "APS-C"?

Canon APS-C is 14.8 x 22.2 mm, or 1.4 and 0.55 "stops" respectively.

They aren't
"stops"
, they are
stops
.

We are discussing the relative efficiencies of sensor area. This is
not
measured in exposure terms.

When we use "stops" in this case we mean: if we increased the exposure of the less efficient sensor by
x
stops, then we would obtain the same noise characteristics (assuming everything else equal etc).

These calculations ignore the additional aspect ratio efficiency of 4:3 over 3:2, which is roughly 4%. This changes e.g. the Canon APS-C to FT ratio from 0.55 to 0.49 "stops", and the 135 to FT ratio from 1.94 to 1.89 "stops".

You lost it there.

No, I didn't.

Refer to my reply to Joe down-thread, where I lay out the calculations for the "conversion efficiency" of the two different aspect ratios.

In the case of FourThirds compared to APS-C we get:

FT is 0.5 (1/2) "stop" less efficient than Canon APS-C (1.6x)

FT is 0.67 (2/3) "stop" less efficient than APS-C (1.5x)

FT is 1.88 "stops" less efficient than 135 ("Full Frame").

Do you really think that calls for an adverb like 'considerably'?

Is 1.2 litres considerably more than 0.73 litres? It's not that far from
double
the amount, Rikke.

Are liters an exponential measure, Boggis?

The exponential nature is irrelevant. One stop appears to
double
or
halve
brightness.

It is the
effect
that is important.

The correct measures are:

If you have 1.2 litres of water (or anything else) you have nearly
double
0.67 litres. An exposure increase of 1.2 stops is nearly
double
an exposure increase of 0.67 stop.

Or, APS-C (1.5×) is
twice as close
to FourThirds in efficiency as it is to 135. APS-C (1.6×) -- at 1.4 and 0.49 "stops" -- is
three times closer
to FT as it is to 135.

Stops are:

exp₂(1.2) = 2.3

exp₂(0.73) = 1.7

2.3/1.7 = 1.35, not even close to double the amount, Boggis.

1.2 stops are 15% more than 1 stop.

0.73 stops are 15% less than 1 stop.

We are talking deviations of less than 1/6. For all practical purposes insignificant. How accurate do you think the labeling of your aperture and shutter speed settings are?

You are (deliberately?) ignoring the practicality of the measure.

The
significance
of the math must be considered, and you can't jump from an exponential to linear method and claim the
unused
linear result is significant.