Simulating depth camera in Unity - unity3d

Question

I am trying to simulate a depth camera in unity. I am using a shader to get the depth textures and I am able to make the camera show this depth image.
The problem now is that the scale extends beyond the closest and furthest objects, going from the near clipping pane to the far clipping plane. I want this to be in grayscale so that the most far object has a color value of 0 and the closest object has a color value of 1, regardless of where those objects are between the clipping planes.
This is a screenshot of what I get:
I am using a shader to achieve this. This is the code of the shader:
Shader "Depth/DepthPostProcessShader"
{
Properties
{
_MainTex ("Texture", 2D) = "white" {}
}
SubShader
{
// No culling or depth
Cull Off ZWrite Off ZTest Always
Pass
{
CGPROGRAM
#pragma vertex vert
#pragma fragment frag
#include "UnityCG.cginc"
struct appdata
{
float4 vertex : POSITION;
float2 uv : TEXCOORD0;
};
struct v2f
{
float2 uv : TEXCOORD0;
float4 vertex : SV_POSITION;
};
v2f vert (appdata v)
{
v2f o;
o.vertex = UnityObjectToClipPos(v.vertex);
o.uv = v.uv;
return o;
}
sampler2D _MainTex;
sampler2D _CameraDepthTexture;
fixed4 frag (v2f i) : SV_Target
{
//get depth from depth texture
fixed4 depthCol = tex2D(_CameraDepthTexture, i.uv);
return depthCol;
}
ENDCG
}
}
}
I am attaching a script to the main camera. This is the code:
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
public class DepthPostProcessing : MonoBehaviour
{
//material that's applied when doing postprocessing
[SerializeField]
private Material postprocessMaterial;
private void Start(){
//get the camera and tell it to render a depth texture
Camera cam = GetComponent<Camera>();
cam.depthTextureMode = DepthTextureMode.Depth;
}
//method which is automatically called by unity after the camera is done rendering
private void OnRenderImage(RenderTexture source, RenderTexture destination){
//draws the pixels from the source texture to the destination texture
Graphics.Blit(source, destination, postprocessMaterial);
}
}
My idea is that I take the distance of the closest and farthest object to make a better scale. I just can't seem to find how to be able to get these properties out of sampler2D _CameraDepthTexture