Why does not perspective projectors work well?

With Unity 5.2.1f1, I'm trying to use a Projector to project an image to a given mesh. I have a simple scene that contains a camera, a directional light source, a plane as the mesh to project things on and a fourth GameObject that has a Projector component.

When I set the Projector to be orthographic, it works pretty good.

But I hope to use it as a mock light source that works on a baked scene, so I wish it to work well when perspective. Now the problem shows up.

My shader on the plane is simply Legacy Shaders/Diffuse, and the shader used for the projector is as follows.

 Shader "Cg projector shader for adding light"
 {
     Properties
     {
         _ShadowTex("Projected Image", 2D) = "white" {}
         _AlphaFactor("Alpha Factor", Range(0.0, 3.0)) = 1.0
         _MainColor("Color", Color) = (1, 1, 1, 0)
     }
         
     SubShader
     {
         Pass
         {
             Blend SrcAlpha OneMinusSrcAlpha
             ZWrite Off
             Offset -1, -1
 
             CGPROGRAM
 
             #pragma vertex vert  
             #pragma fragment frag 
 
             uniform sampler2D _ShadowTex;
             uniform fixed _AlphaFactor;
             uniform fixed4 _MainColor;
 
             // Projector-specific uniforms
             uniform float4x4 _Projector; // transformation matrix from object space to projector space 
 
             struct vertexInput
             {
                 float4 vertex : POSITION;
                 float3 normal : NORMAL;
             };
 
             struct vertexOutput
             {
                 float4 pos : SV_POSITION;
                 float4 posProj : TEXCOORD0; // position in projector space
             };
 
             vertexOutput vert(vertexInput input)
             {
                 vertexOutput output;
 
                 output.posProj = mul(_Projector, input.vertex);
                 output.pos = mul(UNITY_MATRIX_MVP, input.vertex);
                 return output;
             }
 
             fixed4 frag(vertexOutput input) : COLOR
             {
                 // In front of projector and within the boundary of the texture.
                 if (input.posProj.w > 0.0 && input.posProj.x <= 1.0 && input.posProj.y <= 1.0 && input.posProj.x >= 0.0 && input.posProj.y >= 0.0)
                 {
                     fixed4 retColor = tex2Dproj(_ShadowTex, input.posProj) * _MainColor;
                     retColor.a = clamp(retColor.a * _AlphaFactor, 0.0, 1.0);
                     return retColor;
                 }
         
                 return fixed4(0.0, 0.0, 0.0, 0.0);
             }
 
             ENDCG
         }
     }
         
     Fallback "Mobile/Diffuse"
 }

This shader comes from the internet, and the main change I made is adding x and y restrictions to the if statement in the fragment function, because I don't want the clamp or repeated effects of the projected image is shown anywhere outside the frustrum. So is there anything I can do with matrices and apply them to the boundary of the if statement? Or, am I totally doing wrong?

Thanks.