Is my normal interpolation perspectively correct

I am trying to implement a software renderer

It looks like this, it seems my interpolated normal is not perspectively correct

I use scanline conversion and calculate normal with following steps:

Assume we are now drawing line AB (A B have same y value in screen space)

1. Calculating normal of B by interpolating normals of Top vertex and bottom vertex. (Alpha and Beta value is retrieve from top and bottom in screen space)

2. to calculate A is similar

3. draw line AB. Calculating the normals of fragments by interpolating normals of A and B

4. calc light contribution

Sorry for my bad english, hope the picture helps

If I am doing wrong, how to do correct interpolation?