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Short version of my question: How can I compare cameras with different optical zooms and different megapixels (more megapixels can allow cropping for a fake zoom effect) in order to tell which camera can achieve an equivalent of a 5MP image shot with full zoom (x10 --> 360mm) on my SX120 IS?

Long version: I own a Canon SX120 IS (1/2.5", 10MP, 36–360mm, F2.8–4.3). Lately its image quality in medium to low light has become insufficient for me. As I understand, this can be resolved by getting a camera with a larger sensor, 1" for example.

I still want a compact camera (including lense, without having to carry other lenses) but won't get a mirror-less camera since I don't want to give up the x10 zoom ability. I am, however, willing to compromise a little bit in that area.

It seems as if the Panasonic Lumix DMC-ZS100 (1", 20MP, 25–250mm, F2.8–5.9) is almost perfect for me. However, it costs much more than I was planning to pay. My other options are Sony CyberShot DSC-RX100 (1", 20MP, 28–100mm, F1.8–4.9) and Sony CyberShot DSC-RX100 II (1", 20MP, 28–100mm, F1.8–4.9). The problem is zooming with both RX100 cameras isn't as good as with my Canon. They do have a feature called Smart Zoom that crops the image, so instead of a 20MP image you get, 5MP or 10MP. That should be enough for me, and it's not ordinary digital zoom as the details are maintained. Yet, I don't know how it compares against my SX120 IS. Sony's article states the Smart Zoom cropped to 5MP is equivalent to X7.2 zoom, but that x7.2 is what it would be like if that same camera actually had that zooming ability.

How can I compare the zooming ability using Smart Zoom to my own SX120 IS?

  • Additionally, RX100 III is better than all of those because of full sensor readout during video recording - it uses all sensor data to construct output image. For the same reason Panasonic GH4 is just as good as Canon 5D Mark III - just about same noise levels with one quarter of area. – Euri Pinhollow Jul 3 '16 at 9:02
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    I hardly ever shoot videos so it's not something I'd pay more for. I do still seem to prefer the RX100 over the RX100 II. – shwartz Jul 3 '16 at 10:42
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Cropping and zooming are basically equivalent, so this is easily calculated. Zooming in 2× — like, focal length 36mm to 72mm — is like cutting the frame in half. Of course, that's each dimension, so you need to square it to calculate megapixels. For example, a 24mpix image might be 6000×4000, and to simulate that 2× zoom, you'd cut it in half each way, to 3000×2000 — or, 6mpix.

To zoom in 10×, megapixels get cut by 10², or 100×, so you'd have a 600×400 pixel image — not very much to work with. And, even a 1" sensor isn't very large, so by looking that closely, you're pushing the camera system (lens and sensor) quite a lot, and you probably wouldn't be very happy with the results even for online viewing or small prints where that resolution might otherwise be adequate.

  • But since the RX100 already has optical zoom of x3.6, as I understand, cropping to 5MP results in an overall zoom of x3.6*2=x7.2. So the RX100's 20MP 5472x3648 image will result in a 5MP 2736x1824 which is alright for 10x15cm (4x6") prints, for example. Right? What's I'm not sure of is if I can compare that x7.2 zoom to the SX120 IS's x10 zoom, since they have a different focal length. – shwartz Jul 3 '16 at 8:59
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    @shwartz Don't fixate on the multiplier. Instead, compare the focal length. Use 35mm equivalent values to normalize for sensor size. In your example, to get from 100mm-e to 360mm-e is 3.6×. That means 5472 ÷ 3.6 = 1520 and 3684 ÷ 3.6 = (about) 1024 — so, 1520×1024. – mattdm Jul 3 '16 at 9:45
  • Or to put it another way: 3.6² is about 13, so, 20mpix ÷ 13 = 1.5mpix. This gives you 250ppi for a 4×6" print, which is probably okay — but, again, kind of pushing the limits of the system, so theoretical numbers aside, you may not be happy in practice. – mattdm Jul 3 '16 at 9:52
  • Of course, that's only in cases where you need the extra "reach" — you'll have to judge the importance of that against better image quality zoomed out. – mattdm Jul 3 '16 at 9:54
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However, it costs much more than I was planning to pay.

As the size of the sensor increases the cost of the lens needed to provide an equivalent picture (same field of view, or depth of field, or brightness, etc.) increases rapidly. Not only must the lens be longer in focal length to provide the same field of view, but the diameter of the entrance pupil (effective aperture) must also increase by the same linear factor to provide the same f-number.

The problem is that lens elements are three dimensional rather than linear. To increase the linear size by a factor of two the physical volume of the lens must increase by a factor of 2³=8! This requires eight times as much material to produce such a lens element. Then there is the problem of the increasing size and thickness of the lens elements that increase how the lens refracts the different colors of light slightly differently. Thus the larger the lens, the more it needs corrective elements for chromatic aberration, spherical aberration, etc. Corrective elements in lenses tend to be the most expensive, both in terms of the exotic materials often used and the production costs to form those materials in the exact shape needed for them to work properly.

The larger front lens elements are also needed to gather more light to cover the larger sensor. A lens must collect four times as much light to provide the same density of light (brightness) on a sensor twice as wide. If you just spread the same light coming through the front of the lens onto a sensor twice as wide, you give up two f-stops in terms of exposure. This is exactly what happens when using a 2X teleconverter.

In the end you want just as wide focal length range, better low light performance, and just as inexpensive as your SX 120 IS. You can have any combination of two of those three. But you're not going to find any camera with all three.

  • Thanks for the explanation. I never knew why lenses are such an issue and why they're so expensive. I'm OK with two of the three as I am prepared to pay 2-3 times more than what my SX120 IS used to cost 5 years ago. I've come to terms with the price of the ZS100 but I'm still not sure if I should choose that over the RX100 (and which RX100). I understand low-light image quality, HDR and panorama mode are better in the RX100 (the first being most important), but still can't tell if its zoom can be sufficient (when 20MP x3.6 zoom cropped to 5MP) compared to my SX120 IS. – shwartz Jul 3 '16 at 9:47
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If you are considering a camera with P pixels, and you have a minimum after-crop megapixel count you are considering (Pmin), then the digital zoom ratio of the camera is ZD = √(P / Pmin).

Just multiply this digital zoom ratio by the lens's optical zoom ratio to get the total zoom ratio. Thus for the RX100 cameras, their optical zooms are 100/28 ~= 3.6×. With their 20MP sensors cropped to 5MP, the digital zoom is √(20/5) = 2. So indeed, their total zoom ratio is just shy of 7.2×


You asked in a comment,

Can that x7.2 zoom be compared with the x10 zoom of my SX120, considering their focal lengths are different?

Zoom ratios are not a good metric for comparison between different lenses / cameras (other than as marketing bullet points). As you mention, let's just look at their focal lengths.

First, it's important to note that the focal lengths listed in the specs for most compact cameras are 35mm full-frame equivalent focal lengths.

The optical zoom RX100 covers the 28mm–36mm range that your SX120 doesn't. But your SX120 covers the 100mm–360mm that the RX100 doesn't reach. In terms of zoom ratios, the RX100 and SX120 cover the same 2.8× zoom ratio in the 36mm-100mm range. The remaining 3.6× of your zoom range (10/2.8) is in the telephoto region, whereas the remaining 1.3× of the RX100 zoom range is in the wide angle region. Even with digital zoom / "smart zoom", the RX100 can only reach to a virtual 200mm (and that's at 5MP).

Quite simply, your camera has much longer native "reach" without resorting to digital zoom / cropping. The RX100 has a wider view at the wide end of the zoom range, and even at its longest zoom with in-camera cropping, doesn't have the "reach" of your 10MP 360mm).


How good is Sony's Smart Zoom?

Ignore the marketing of "Smart" zoom (other brands use "Intelligent Zoom", "Safe Zoom", etc.). It is just cropping, plain and simple.

At Sony's support site, "What is the difference between Digital Zoom, Clear Image Zoom and Smart Zoom?" says:

With standard digital zoom, pictures captured by the image sensor of the camera are enlarged using digital signal processing. Therefore, as the magnification level increases, signals to be estimated also increase and can reduce the image quality.

When using Clear Image Zoom, however, zoomed images are captured close to the original quality when shooting a still picture. The camera first zooms to the maximum optical magnification, then uses Clear Image Zoom technology to enlarge the image an additional 2x, producing sharp clear images despite the increased zoom ratio.

The Smart Zoom™ feature allows images to be zoomed without losing picture quality. The central part of the picture is trimmed and enlarged without image processing.

Taking them at their word ("without image processing"), Smart Zoom is just cropping.

  • By the time you put a slow lens such as one of the 18-200mm lenses you mention on the camera you've already given back the low light performance advantage of the larger sensor compared to a smaller sensor with a faster lens. – Michael C Jul 3 '16 at 8:26
  • I'm sorry. I should have mentioned that I don't want to pay extra for special lenses and that I don't want to carry different lenses but just have the camera ready for what I could do with my SX120 IS, but also get better photos in low light. I updated the question. Thanks for the formula. Can that x7.2 zoom be compared with the x10 zoom of my SX120, considering their focal lengths are different? – shwartz Jul 3 '16 at 9:19
  • @MichaelClark the lenses I listed give up 2/3 - 1 stop (from wide to fully zoomed) compared to the SX120, and only give up less than a quarter stop at the farthest reach compared to the Panasonic shwartz was considering in OP. But the low light performance of say, a Sony a5100, with either of the lenses I mentioned still outperforms the Lumix (and certainly the older Canon SX120). – scottbb Jul 3 '16 at 12:44
  • True, but you're still giving up a lot of the low light performance you could get with the same sensor and an f/2.8 or faster lens. You're also giving up the compactness and affordability the OP desires. An a5100 + Sony 18-200 is going to set you back around $1,300 and can't fit in most pockets. – Michael C Jul 4 '16 at 1:45

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