The alpha channel is a black & white image containing information about where a specific object exists and where it does not. White in the alpha represents an object, black represents empty space. It is useful as a clipping mask when you want to isolate an object and composite it with another object (for example: clipping a car render and pasting it over a photograph).
Opaque option
With transparent objects the alpha normally takes into account the amount of transparency of the object and renders with varying degrees of grey - for example very dark grey for very transparent objects. It is possible to render a completely white alpha also for transparent objects with the Opaque option. This can be useful if you want to maintain the full look of the transparency from the render, instead of blending it with any other images in your composite. 
From left to right: Render, Alpha with opaque option OFF, alpha with opaque option ON
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This step is important, otherwise you may see a thin white line between your objects and any background you cut out objects into. |
Option 1: Selecting only one of the channels in the alpha. Select one of the channels in the channels palette. Then Ctrl+A to select all, then Ctrl+C to copy.
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Option 2: Converting the RGB alpha into greyscale. Make sure the alpha image is the active document in Photoshop and go to Edit>Convert to Profile and choose sGrey from the drop down list and click OK. Then select the entire alpha image with Ctrl+A, then Ctrl+C to copy it.
Step 3
In the render image, switch to the channels palette, create a new channel and paste the alpha channel in this new channel (Ctrl+V). Next, hold down Ctrl and click on the thumbnail of this new channel - this will load it as a selection.
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An example showing why this is necessary:
Comparing two renders - with/without a black background. Both renders would produce the same alpha map and the illumination on the sphere itself is exactly the same. The sphere has been rendered deliberately out of focus to show what happens at the edges of objects (which always fade into the background even when in perfect focus because of the antialiasing applied). 
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The first sphere has a background which changes in brightness and the out of focus parts of the sphere mix with this changing background. After using the alpha to cut it out of the background, those areas with changing brightness remain. It is not possible to remove them using either "remove black matte" or "remove white matte".
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