Layer looks different when exported alone

Question

I'm having a little bit of trouble exporting a bunch of semi-transparent layers from a PSD file in Photoshop.

If I export the layers alone one by one (by hiding all other layers) and compose them in my app they look different, e.g. they seem to have less transparency or more white color in them.

I've been googling about this issue for a while now and so far I only know that is has something to do with layer blending.

Is there a way to export the layers so that they will look the same when I bring them all together?

Edit:

Here are some screenshots:

Design in photoshop:

Inside the app (after exporting and combining same layers):

Answer 1

Both screen and overlay are easy to implement, Wikipedia lists formulas for all of the modes. Screen is:

value = 1-(1-Bottom)(1-Upper)

where Bottom is the per channel value of bottom layer and Upper is the per channel value of Upper layer. All colors are assumed to be in 0-1 range. Overlay is listed as:

value = Bottom*Upper*2 if Bottom < 0.5
value = 1-2*(1-Bottom)(1-Upper) if Bottom >= 0.5

Now this is all easy to implement if you have a environment where you can actually manipulate things like this, such as a game etc. However if you work on a webpage or other scene graph system with no shader access then you end up in a situation where you can not easily dominate the object model to do your bidding without taking a undue amount of the effort to your own name. But that is a question for stackoverflow.