Obviously the biggest hybrid zoom on the market (Nikon Coolpix P900 I think) does not range from actual 24 mm to 2 meters in physical length, but what kind of optical systems do manufacturers use to bring optical zooms to such high (83x) levels?

These high zoom hybrid cameras are relatively cheap compared to regular DSLR super telephoto lenses, so it does not look like they use the same expensive optical elements at all. They manage to pack 83x in 20cm or so, while the best 600mm DSLR lenses are about twice longer for about 12x, so I wonder how they do it, how much light is lost in the process, etc.

Another thread about P900 artifacts makes me wonder if what they claim to be 83x "optical" zoom includes some electronic processing.

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    I'll remove the side question as Stack Exchange strongly prefers only one question per post, but it's answered by Can I convert binocular zoom to equivalent lens focal length?. – Philip Kendall Jul 12 at 12:27
  • Isn't that just a crop sensor that is doing "all the work". The actual optical part of the optical is probably below 10 mm at the widest and then just 83x that is the telephone focal length. – Andreas Jul 12 at 12:44
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    @Andreas It's actually 4.3 mm-357 mm. – Michael Clark Jul 12 at 16:22

I think the use of the term 83X while true, is most misleading. The Coolpix does a remarkable job when it comes to its optical range which is 83X. This is actually called the zoom range. The math is: The power of the camera’s lens is adjustable from 4.3mm wide-angle to 357mm telephoto that’s 357 ÷ 4.3 = 83. In other words the span of the zoom is 83X.To accomplish the lens is constructed using 16 individual glass lenses. Some are glued together, some are air-spaces. There are 12 lens groups each air-spaced apart. When you zoom, the air-space distance changes and this act cause the power of the lens to change. The span of the zoom is from wide-angle at 4.3mm to telephoto at 357mm.

When photographers discuss their lenses, the fact that the zoom range covers 4.3mm thru 357mm is little understood. This is because a far larger film camera is used as a yardstick that defines lens performance. This is the 35mm film camera that has been with us for nearly 100 years. Because of its popularity, we talk about camera lenses in terms that actually apply only to these venerable camera types. However we can make comparisons

It goes like this: The Nikon Coolpix P900 is a super miniature camera thus it makes miniature images that are only about 18% of the size of the esteemed 35mm camera. The 35mm is actually 5.6X larger. So we multiply 4.3 X 5.6 = 24 and 357 X 5.6 = 2000. Now we can say this Coolplix performs as if the zoom range is 24mm – 2000mm. Now 50mm is considered “normal”. A lens shorter is termed “wide-angle”. A lens longer is termed telephoto. Since 50mm is “normal” at full zoom which is the equivalent of 2000mm, objects will appear 2000 ÷ 50 = 40X larger. In other words a bird in the tree 1000 feet away will image as if it were only 25 feet away.

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    Note that the crop factor is a comparison of linear measurements. In terms of area, a 35x24mm FF sensor is about 30X larger than the sensor on the P900. – Michael Clark Jul 12 at 16:21
  • To those wondering: 1/30 = 0.18^2 (approximately, but it's a decent approximation). – BallpointBen Jul 12 at 20:41
  • The industry standard is to compare differences between frame sizes, format A to vs. format B; by comparing differences in the diagonal measures. This value is known in the industry as the magnification or crop factor. The differences in area are also valuable. However, focal length equivalency is based on the crop factor. The use of the diagonal when advertising angle-of-view inflates and thus helps sales. This is the same tactic used when advertising TV sets; the diagonal measure is given because it inflate the advertised size of the set. – Alan Marcus Jul 13 at 16:19
  • I didn't realize the size of the sensor was so much smaller, 1/2.3" does not really talk to me and their camera cases are not very small either. I understand now better how the Coolpix's zoom can get to 83x (P900) or 125x (P1000): The lenses are much smaller and therefore much cheaper, so you can add more of them and still stay on budget. – Chimel31 Jul 13 at 20:49
  • Sometimes math misleads. Say a binocular delivers 10X magnification. One could truthfully say the “area magnification” is 100X. It all depends on how you see such things. The Nikon P900 sports an image sensor that measures 4.55mm height by 6.17mm length. The diagonal of this rectangle is 7.67mm. The area of this rectangle is 28.07mm sq. The esteemed 35mm fill frame which is the basis of comparison measures 24mm height by 36mm length. Its diagonal is 43.27mm. Its area is 864mm sq. Comparing diagonals the P900 is 17.7% the size of the FX. Comparing area, the P900 is 3.25% the size of an FX. – Alan Marcus Jul 14 at 21:01

How do they get to 83x?

Sensor size (1/2.3"), physical length, loss of aperture (f/2.8-8).

Sensor Size

The Samsung S9+ phone uses a 1/2.55" sensor, the Nikon P900 and P1000 use a 1/2.3" sensor.

Obviously the biggest hybrid zoom on the market (Nikon Coolpix P900 I think) does not range from actual 24 mm to 2 meters in physical length, but what kind of optical systems do manufacturers use to bring optical zooms to such high (83x) levels?

Lens Focal Length:

P900: 4.3-357mm (angle of view equivalent to 24-2000mm lens in 35mm format) 67mm Filter

Lens f/-number: f/2.8-6.5, Lens Construction: 16 elements in 12 groups, Lens Zoom: 83x

P1000: 4.3-539mm (angle of view equivalent to 24-3000mm lens in 35mm format) 77mm Filter

Lens f/-number: f/2.8-8, Lens Construction: 17 elements in 12 groups, Lens Zoom: 125x

P1000

Length, with body, unzoomed: 7.2 in. (181.3 mm). Fully zoomed doubles that.

These high zoom hybrid cameras are relatively cheap compared to regular DSLR super telephoto lenses, so it does not look like they use the same expensive optical elements at all. They manage to pack 83x in 20cm or so, while the best 600mm DSLR lenses are about twice longer for about 12x, so I wonder how they do it, how much light is lost in the process, etc.

200-500mm

Nikon AF-S 200-500mm f/5.6E ED VR, 95mm filter. Approx. Dimensions (Diameter x Length): 4.2 in. x 10.5 in. This lens doesn't double it's length when zoomed nor is it as dark or long a zoom; also it costs U$1300, more than a P1000 U$1000, or over twice the price of a P900 U$600.

Lens f/-number: f/5.6, Lens Construction: 19 elements in 12 groups, Lens Zoom: 200 / 35 = 5.71 and 500 / 35 = 14.29 if you want to compare it that way.

Sigma 300-800mm

Sigma 300-800mm F5.6 HSM APO CONV EX DG D, 46mm rear filter, Approx. Dimensions (Diameter x Length): 6.2 x 21.3 in. Lens Construction: 18 Elements in 16 Groups. Lens Zoom: 300 / 35 = 8.57 and 800 / 35 = 22.86 if you want to compare it that way. Price U$8000 (available Aug 2018).

Compare those consumer lenses with a professional lens, the Fujifilm UA107x8.4BESM.

UA107x8.4BESM

Fujifilm UA107x8.4BESM 8.4-900mm and with built-in 2x extender 16.8-1800mm, that's 214x. During a football game a camera a 1000 feet away will appear to be less than 5 feet away. Filter size: over 250mm (10 inches), HT-EBC coating and stabilized. It has a f/1.7 aperture at 8.4-340mm, reducing to 4.5 at 900mm, with the 2x it drops to f3.4-f9.

Height x Width x Length: 258x264x610mm. This doesn't change length when it zooms and has various preset, focus and zoom options. Designed for a sensor size of 9.6 x 5.4mm (2/3") it has a crop factor of around 4x compared to full frame. Available for only U$198,750, plus shipping.

... how much light is lost in the process, etc.

You lose almost half your light and considerable image quality, and a lot of length and weight, by choosing a bridge camera over a DSLR; along with a lot of other considerations.

Another thread about P900 artifacts makes me wonder if what they claim to be 83x "optical" zoom includes some electronic processing.

When they say optical that's what they mean, the P900 and P1000 have 4x digital zoom.

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    "Lens Zoom: 200 / 35 = 5.71" Sorry, why 35? – Chimel31 Jul 13 at 20:55
  • @Chimel31 - Why? for example 35mm - Full frame sensors are slightly different sizes between different manufacturers. "Full frame" sensors are: 36x24, 35.9x23.9 or 35.9x24mm -- Wikipedia: "Image Format": "The term 135 format usually refers to a 36×24 mm film format, commonly known as 35 mm format. The 36×24 mm format is common to digital image sensors, where it is typically referred to as full frame format.". – Rob Jul 14 at 0:39
  • Errrr.... Your latest addition is not a "professional lens". It's a sports broadcast lens not intended for photography. – mattdm Jul 14 at 3:50
  • @mattdm - Chimel31 asked about hybrid cameras and said: "... it does not look like they use the same expensive optical elements at all. They manage to pack 83x in 20cm or so, while the best 600mm DSLR lenses are about twice longer ...". So it's an "Optical Question", how do they do it? As opposed to a question about the body of the P900. Fujifilm consumer lenses are considerably less expensive than their professional lineup and located on a different section of the website. I don't think the addition worsens the answer. – Rob Jul 14 at 4:14
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    @Rob 5 - You just described the full frame format, which I know very well, but not why you divide the focus length by 35 to get a "lens zoom." Shouldn't it be 500/200=2.5 to get the zoom level, or 500/50=10 to get the magnification level? – Chimel31 Jul 14 at 5:54

Let's start with the basic idea of a fairly simple zoom. For example, we can start with three elements. The and rear and magnifying elements, and the middle is a reducing element. The magnifying elements bring the rays of light together. The reducing element spreads them apart.

So, if we move the middle element all the way to the back by the rear element, the light goes through the front element, so the light rays start coming together. The keep coming together for quite a ways, until they get to the reducing element, which spreads them apart--but since it's right by the rear element, they don't spread much before they get to the rear element, and start to come back together again. So, the rear element basically takes almost everything that came through the front element, and brings it into focus on the sensor, giving quite a wide angle view.

On the other hand, if we move that middle element right up by the front element, the light goes through the front element, comes together a tiny bit, then goes through the reducing element so it immediately starts to spread back out. It spreads out quite a bit before it gets back to the rear element. So, only a little bit of the center of the picture that came through the front element hits the rear element, and only that small part of the picture is brought into focus on the sensor, so we get a much narrower view. With that design, the zoom ratio is limited by the distance between the front and rear elements though--to get to 83x zoom, we'd need a lens that was physically extremely long.

To get to a higher zoom ratio, we basically replicate that basic idea a number of times over. For example, let's think of each of those three elements being replaced by a set of three elements, so we not only move the middle group from the front to back, but also vary the level of magnification or reduction each of them provides.

Let's assume that the original gave a 3:1 zoom ratio. With each element replaced by a group of three elements that itself gave a 3:1 ratio, our overall ratio would theoretically be something like 3x3x3 = 27x. Add a fourth similar group and we're at around the 80x range (or so).

To get quality sufficient for even a low end camera, you need to do a fair bit more than that. Even a fairly cheap lens will use different types of glass in the different elements to help reduce chromatic aberration, probably some aspheric elements to control spherical aberration, and so on.

Nonetheless, the basic idea of all zooms mostly comes down to that fairly simple situation of having (at least) one magnifying element and one reducing element, and moving them relative to each other. Getting to high zoom ratios mostly means replicating that basic idea a number of times, and doing enough more to keep aberrations, distortions, etc., at least somewhat under control.

There's a bit more than a single question in your query. Focusing on the first one:

Obviously ... [the] Nikon Coolpix P900 ... does not range from actual 24 mm to 2 meters in physical length, but what kind of optical systems do manufacturers use to bring optical zooms to such high (83x) levels?

Firstly, don't confuse the 35mm equivalent focal lengths (24mm–2000mm) with the actual focal lengths of the P900's lens, which ranges 4.3mm–357mm. For more on this, see the related question, What is crop factor and how does it relate to focal length?

Still, you are right, obviously the physical length of the P900's lens is not so short as 4.3mm, nor as long as 357mm. So we need to address the fundamental question, what is focal length?

If you could replace the P900's wide-angle focal length with single symmetric lens glass (like a magnifying glass) with the same magnification as the P900's wide end, then parallel light rays coming into that single-element lens would focus at a point 4.3mm, nearly one-sixth of an inch, beyond the lens. That's what focal length means.

The real lens of the P900 isn't that short. All real-world lenses have multiple optical elements in them. These elements work together to bend and "unbend" (diverge) the light rays several times. The point of these multiple elements (and groups of elements) are:

  • to allow the lens to focus, rather than moving the entire lens assembly in or out to focus (these elements comprise the focus group(s));
  • to allow the lens to zoom — i.e., change focal length;
  • to control aberrations such as chromatic aberration (which is a natural consequence of light bending through materials with different refractive properties).

So lens designers add a lot of elements to make the lens more useful than a narrow range of operating conditions. That adds length to the lens assembly, but in the case of wide angle lenses, it is optically "equivalent" (using that word loosely) to a simple single-element lens with a focal length shorter than the real-world lens's physical length.

Similarly, at the other end of the P900's zoom range, at 357mm focal length, the lens is physically less than 357mm long. That's because the lens has a telephoto group, a group of elements that allow a lens to be physically shorter than its thin lens –equivalent focal length would dictate. See also, What is the difference between a telephoto lens and a zoom lens?


Now, as far as, how do they specifically get zoom ranges as high as 83x (or even more, such as the 125x zoom in Nikon's recently announced P1000), well... science. Magic. A little bit of both?

These high zoom hybrid cameras are relatively cheap compared to regular DSLR super telephoto lenses, so it does not look like they use the same expensive optical elements at all. They manage to pack 83x in 20cm or so, while the best 600mm DSLR lenses are about twice longer for about 12x, so I wonder how they do it, how much light is lost in the process, etc.

Regarding comparing zoom amount vs. lens length, remember to compare like vs. like. In this case, the Square-cube law (Wikipedia) comes into play: as an object is scaled in size by a factor S, its surface area is scaled by S², and its volume is scaled by S³.

The P900 has a crop factor of 5.6, meaning the linear scale factor between cameras like the P900 with a 1/2.3" sensor and 35mm full frame cameras is S = 5.6 (from P900 to 35mm FF). So, to create "equivalent" optical systems (as far as the geometry of the optics is concerned), the scaled-up P900-type 83x lens, but made for a 35mm FF body, would:

  • have roughly a 5.6 times larger diameter, and
  • weighs roughly 5.6³ = 175 times the weight of the P900 lens!1

    Note 1: The lens probably wouldn't weigh quite that much; a simple S³ scaling implies all components, including focusing motors, lens tubes, focusing helixes and controls, etc., scale their wall thickness 5.6 times. That's not necessary, there'd be plenty of weight to shave. But, from an optics standpoint (without changing the optical formula), the weight of the glass would scale by S³.

And note that even just the length of the ~20cm lens scales up by S to about 112cm — that's over a meter long.

I don't even want to know how the cost would scale, but 175x the $1000 cost of the new P1000 actually wouldn't be totally out of line for such a ludicrously monstrous beast if it were for 35mm full frame bodies.

After that, there have been several different one-of-a-kind -type lenses that went for astronomical prices, but let's not get ridiculous (!).

So there are obvious nonlinear cost benefits to scaling down. But since the P900 and P1000 aren't aimed at the high-end professional or prosumer market, they can make further cost-savings decisions, such as:

  • using lower-quality optical glass in some of the lens elements;
  • reducing the number of optical coatings (such as low-dispersion and anti-reflective);
  • eliminate weather sealing;
  • provide less warranty coverage;
  • and all of the other usual suspects when companies engage in market segmentation.
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    The canon 50-1000 cine lens might also be a good example of what happens to size and price. – lijat Jul 13 at 9:31
  • "Focusing" on the first one… chuckle, chuckle. – Stan Jul 13 at 18:34
  • @Stan heh, that one was completely unplanned. Didn't even notice until you did. – scottbb Jul 14 at 0:59

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