According to the research paper Multidirectional Scratch Detection and Restoration in Digitized Old Images, we have,

$$H(u, v) = \frac{1}{1 + 0.414 {. \sqrt[{2n}]{\frac {u^*}{D_u}+\frac {v^*}{D_v}}}} \tag{1}$$

where:

\begin{align} u^* &= \cos \theta . (u + t_x) + \sin \theta . (v + t_y)\\ v^* &= -\sin\theta . (u + t_x) + \cos \theta . (v + t_y)\\ t_x &= \mbox{center}_x \times \cos \theta\\ t_y &= \mbox{center}_y \times \sin \theta \end{align}

The above formula generated a kernel of the following data:

The convolution operation is generating a complete black image. My guess is, the kernel values are too small.

Is there any technique to magnify these data?

N.B.1. I have actually corrected formula $(1)$

N.B.2. I have used an 8-bit-indexed gray-scale image and a 32x32 mask. I padded the mask. Then converted both the image and the mask to complex 2d array. Then I applied Fourier transform to both of them. Then I multiplied them. Then did the Inverse transform. I have tested with $\theta=0.9$ and $radian=0.9$. The results are not coming as expected.