Ray casting in Unity, matching Unity camera parameters

I'm trying to do some ray casting in a pixel shader.

I'm doing this by drawing a screen aligned quad using an orthographic projection, but I would like the ray casting to match the camera parameters of my main Unity camera - a perspective camera with a 60 degree field of view.

I'm having trouble calculating my Ray Direction to match this.

Here is the pixel shader code I'm using.

 // fragment.hPos is output from the vertex shader - is the model-view-projection of the 
 // vertex coordinate
 float4 p1 = fragment.hPos / fragment.hPos.w;
 float screen_x = (p1.x + 1) * (_ScreenParams.x/2);
 float screen_y = (p1.y + 1) * (_ScreenParams.y/2);            
 // fragcoord is supposed to be the same as openGL's gl_FragCoord
 float2 fragcoord = float2(screen_x, screen_y);
 
 float i =fragcoord.x;
 float j = fragcoord.y;
 
 float fovx, fovy;
 fovx = 1.04719755; //60 degrees horizontal field of view
 fovy =  _ScreenParams.y /  _ScreenParams.x * fovx;
             
 //holds the x and y coords of the viewplane point
 x = 0;
 y = 0;
 x = (((2* i) - _ScreenParams.x) / _ScreenParams.x) * tan(fovx);
 y = (((2*j) - _ScreenParams.y) / _ScreenParams.y) * tan(fovy);
 
 // ro = ray origin, at the camera position
 ro = cameraPosition;
 float3 rd = float3(x,y,1.0) - ro; // rd = ray direction viewPlane is at x, y, 1.0
 rd = normalize(rd);

When I go on to use this ray origin (ro) and ray direction (rd) to ray cast the scene, the result doesn't match the scene view from a regular unity camera. Objects aren't in quite the same position and look 'stretched' vertically.

Anyone know how to do this correctly? I would greatly appreciate any guidance. Thank you!