Why does a multiplied texture with alpha loose detail information? The left image shows the texture mapped to a plane, the right one is original image in the UV Editor. The rendered image looks extremely blurred. What would be the correct material and texture settings to have only the alpha part (check pattern right) invisible?

.blend file



Material and texture settings are:
Setting the Blend Mode to multiply isn't necessary. 

Material Settings:


Specular


Intensity: 0.0 


removes this: 
Transparency: On 


Method: Z Transparency
Alpha Slider 0.0



Texture Settings:


Type: Image or Movie
Image: The Texture Image
Use Alpha: On (Otherwise darker parts of the image which are supposed to be opaque will be partially transparent)
Image Sampling


Alpha: Use : On (Otherwise darker parts of the image which are supposed to be opaque will be partially transparent)                   

Mapping


Coordinates: UV
Map: UVMap

Influence


Color: On (1.0)
Alpha: On (1.0)

Blend: Mix (Default)


Settings to compare:




Result (left rendered, right image editor)
Image source by Luc Viatour / www.Lucnix.be



Result zoomed