$\text{}w=z\lambda /d$

Where:

$w$: Distance between fringes

$z$: Distance from slits to screen.

$\lambda $: Wave length of light

$d$: Distance between slits.

Now, looking at the setup from a reference frame traveling in the direction of the distance 𝑧 between slit and screen and moving away from the slit in direction of the screen, the light gets redshifted and the distance 𝑧 gets Lorentz contracted:

$\text{}{w}^{\prime}=\frac{z}{\gamma}\gamma (1+\frac{v}{c})\lambda /d=z(1+\frac{v}{c})\lambda /d$

This only holds for the first fringe or so, that aren't too far from the center, because the red-shift formula changes farther out. However, it's obvious that the distance between fringes has increased!

Where is my mistake?