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Comparing a P&S to an APS-C camera: SNR, Framing/Equiv. Zoom range, DOF
Posted By: dosdan, 06-03-2011, 05:00 PM

Alright so all I know so far is DSLR can take bokeh photos. But how about if I want to take a photo like a point and shoot camera will. What lens will I need to use? For example, taking a group photo. Taking a nice view without any part of the photo being out of focus.

The above question shows the typical concerns that a P&S user faces when they upgrade to a DSLR. What are the differences between the two formats?

A P&S has a much smaller sensor area compared to a APS-C DSLR. See the table here: Image sensor format - Wikipedia, the free encyclopedia

Some of the consequences of the bigger sensor on APS-C compared to P&S are:

1. Less noise. DSLRs typically have 2.5-3.5 less stops of noise i.e. can be used with a 5.6-11 times higher ISO for the same S/N ratio (SNR). So the noise of a typical P&S at ISO 100 is the same level as a DSLR at ISO560 or higher. Now, the P&S hides this by heavier NR, particularly at higher ISOs. The Dynamic Range (DR - the ratio of the brightest light level, able to be captured before the sensor saturates, to the noise floor) of the P&S is correspondingly lower than for a DSLR.

For example, comparing Canon G12 1/1.7" P&S to the Pentax K-5, there is a 2.9 stops difference in SNR at ISO100 & ISO200. Looking along the orange horizontal 32 dB SNR line, you can see that the G12 reaches this SNR value at manufacturer's ISO100 (true ISO93), and is almost 3 columns (stops) distant from the same 32dB SNR of the K-5 at ISO800 (true ISO717) to the right.

For figures comparing the SNR within & across different formats see:

For an explanation of exposure settings and photographic stops (by far, the easiest way to understand exposure parameters) see:

2. Different "magnification" / "crop factor" between different formats. Consider a lens that has a 36mm exit pupil (the diameter of the circle of light when the lens is projecting an in-focus image onto a plane i.e. the image sensor or a piece of paper.

From the image sensor table:

Format Sensor Width (mm)
FF 36
APS-C 23.6
APS-C (Canon) 22.2
P&S (1/2.3") 6.2

Let's assume that a group of 6 people was standing shoulder to shoulder in one rank. Now you move back so your FF camera just frames the width of the 6 people. So the width of the projected image of this group is 36mm (the width of the FF sensor). (Actually the diameter of the cone of light will be wider than 36mm since we're fitting a rectangular sensor into a circle of light, but to keep things simple, pretend that it's a circular sensor.)

Put the same lens on the APS-C and now 12mm of the 36mm diameter cone of light will fall outside the width of the 24mm APS-C sensor. So now you have 4 persons fully filling the frame width.

If it were possible, put the same lens on the P&S with a 1/2.3" sensor. Only 6mm of the cone of light falls on the small sensor, with the rest projected outside the periphery of the sensor and so is of no use. Now only 1 person fills the width of the sensor.

So, as the same lens is used on formats with smaller and smaller sensors, the image appears to "zoom in" more. Really, each person is still 6mm wide on the sensors in this example, so more of them can fit on the width of the bigger sensors. But it appears to the user that the same lens on a P&S camera in this example zooms in 6x compared to its use on the FF (or 4x compared to the APS-C). This apparent magnification is called the "Crop Factor" (CF). CF is compared to the FF width, so an APS-C camera has a 1.5x approx. CF (36mm/23.6mm) and a 200mm focal length (FL) lens on an APS-C camera will give the same magnification/angle-of-view as a 300mm FL lens on a FF.

This is also the reason why it is relatively common to get high max. zoom levels with the small sensors in P&S cameras and in most consumer video camcorders.

Say you're used to using a P&S with a 4x zoom lens. The lens has a 5mm-20mm FL range. This is the 4x change in FL as you zoom in. With the relative difference in CF of about 3.7x (5.6 CF of P&S / 1.5 CF of APS-C), on a APS-C you would need a 4x lens that had a FL range of 18.5mm-74mm.

So if you find you can usually frame a group with the 5mm FL "wide-angle" end of this P&S's zoom range, you would need a zoom or prime (fixed FL) lens on an APS-C with a 18mm FL to achieve the same framing.

In this example, I've used the values for the Canon PowerShot SD1300 1/2.3" P&S (Canon PowerShot SD1300 IS / IXUS 105 / IXY 200F: Digital Photography Review). It states that the "equiv. FL" is 28mm-112mm, but that's compared to the Field of View of FF, whereas we're comparing it to APS-C.

3. The Depth of Field changes as the sensor size changes.
Consider the 5mm FL 1/2.3" P&S vs 18mm FL APS-C wide-angle example mentioned above. I'll use the K-5 as the APS-C example and Canon PowerShot SD1300 1/2.3" P&S again.

Using the DOF Calculator: Online Depth of Field Calculator

The subject is at 3m:

APS-C 18mm FL f/3.6 (close to f/3.5 which is the typical max. f-number of a kit lens at 18mm FL) = 1.8m-8.7m DOF range.

P&S 1/2.3" 5mm FL f/2.8 (max. f-number at 5mm FL for the SD1300) = 1.1m-Infinity DOF range.

So with the same framing, at the same distance, the P&S has much more DOF. This is why many P&S shooters don't have much experience with DOF issues, but have to consider it when they upgrade to APS-C.

To get approx. the same DOF range on the APS-C camera with a 18mm FL lens we would need to stop down to f/9 = 1.1m-Infinity DOF range.

By the way, the difference in stops to get the same DOF with both cameras is approx. 3.4 stops, because f/2.8 -> f/4 (-1 stop) -> f/5.6 (-2 stops) -> f/8 (-3 stops) -> f9 (-3.4 stops). This is related to the ratio of the sensor areas, the same reason for the 2.5-3.5 stops SNR difference I mentioned at the beginning.

Older P&S cameras will have very small sensors so the difference can be even greater than 3.5 stops, particularly when compared to an excellent DSLR performer like the K-5. For example the Canon A75, circa 2004, had a 1/2.7" sensor. The theoretical difference in SNR compared to APS-C, based on sensor area, is 4.1 stops. However technology has advanced since 2004 and the actual SNR difference may be greater.


Last edited by dosdan; 06-05-2011 at 03:46 AM.
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06-07-2011, 04:21 PM   #2
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This needs to be simplified a great deal to make it readable. Many extraneous factors are introduced, so that no-one not already familiar with this material could make sense of it.
06-11-2011, 06:39 AM   #3
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Disregard, wrong link.

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