What are Multi-Zone/Matrix metering, Center-Weighted metering, and Spot metering? What about Partial?
Is there a good rule of thumb, or a few pointers, on when best to use each exposure metering mode?
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Matrix is Nikon's multi-segment system. Other companies call their versions Evaluative or something similar. It is the mode you use when you don't want to think about metering. It is very sophisticated and does a good job in most situations.
Spot is used when you KNOW what part of the scene is going to be your midtone, that is the part of the scene that you want to show as 18% luminance. In that case you must point the spot meter at that part and lock the exposure using either the AE-L button or half-pressing the shutter (most cameras are setup like this initially but you can change that). Then you reframe (without releasing the shutter or AE-L button) and take your shot.
Center-weighed is basically the ancestor of Matrix metering. It tries to make the central part at least 18% bright but will vary the results depending on the brightness of the surrounding areas.
To answer your question:
Matrix mode is where the camera tries to match the scene against a database and make an intelligent decision. This is particularly useful for typical tricky situations, like portraits with a bright sky in the background. Most modern cameras get this right. The problem is that it's a black box: you have no way of knowing what the camera is basing its decision on, and what it'll come up with. Since even the most sophisticated systems sometimes get it wrong, this can be frustrating. It's also hard if you want to do something other than the expected: if you want that backlit portrait to be a silhouette, you'll probably want to dial in some EV compensation to bring down the exposure. But, without a lot of familiarity with your camera's own matrix mode (which varies from model to model within the same brand), you can't know how much.
Spot metering is most useful when you have time to take measurements of the different key areas in your composition and then consider the overall effect. It measures light in a very small portion of the area — 2%-3% of the frame. Take readings from the areas you care about, and then decide on an overall exposure which takes that into account. (The most simple situation, of course, being when you only care about one area and can let all the rest over or under expose.)
Partial metering is like spot metering, but covers a larger area — typically around 10%. Some entry level cameras lack true spot-metering and offer this instead.
Center-weighted takes most of the frame into account, with less consideration to the edges. This may be because a too-bright sky at the top of the frame is a common situation, but I think it's probably simply because it's cheaper to do than complete, full-frame average. The disadvantage of this mode is that it's dumb -- if anything even slightly complicated comes up, you'll need to adjust EV compensation. But the advantage is that it's completely predictable, so you can easily learn to tell which situations require what kind of compensation.
I don't know if the D60 has this option, but with the Nikon D300s, you can go into the menu custom settings, and set the AF ON button to focus, and the shutter button to meter. They are now separate.
It is all to do with the brightness range in the scene you are photographing.
Where the brightness range is 'normal', that is fits nicely in the range that the sensor of your camera can capture, then Matrix will generally do a good job, producing an exposure with a well centered histogram.
When the brightness range of the scene is very small or very high there is a good chance the camera will wrongly position the histogram of the exposure. In this case, by using spot metering, you are telling the camera which part of the scene should be centered in the histogram. In some cases it is not obvious where you should spot meter and then center weighted metering is a good standby since that will tend to average a region.
The same reasoning applies when the region of interest is close to either end of the brightness range, use spot metering where feasible otherwise use center weighted metering.
http://www.usa.canon.com/dlc/controller?act=GetArticleAct&articleID=2666 also discusses this topic.