I'm trying to apply fog of war to areas on the screen not currently visible to the player. I do this by rendering the game content in one RenderTarget and the the fog of war into another, and then I merge them with an effect file that takes the color from the game RenderTarget and the alpha from the fog of war render target. The FOW RenderTarget is black where the FOW appears, and white where it doesn't.

This does work, but it colors the fog of war (the unrevealed locations) white instead of the intended color of black.

Before applying the effect I clear the backbuffer of the device to white. When I try to clear it to black, non of the fog of war appears at all, which I assume is a product of alpha blending with black. It works for all other colors, however - giving the resulting screen a tint of that color.

How do I archieve a black fog while still being able to do alpha blending between the two render targets?

The rendering code for applying the FOW:

private RenderTarget2D mainTarget;
private RenderTarget2D lightTarget;

   private void CombineRenderTargetsAndDraw()
    {
        batch.GraphicsDevice.SetRenderTarget(null);
        batch.GraphicsDevice.Clear(Color.White);

        fogOfWar.Parameters["LightsTexture"].SetValue(lightTarget);

        batch.Begin(SpriteSortMode.Immediate, BlendState.AlphaBlend);
        fogOfWar.CurrentTechnique.Passes[0].Apply();
        batch.Draw(
            mainTarget,
            new Rectangle(0, 0, batch.GraphicsDevice.PresentationParameters.BackBufferWidth, batch.GraphicsDevice.PresentationParameters.BackBufferHeight),
            Color.White
        );

        batch.End();
    }

The effect file I'm using to apply the FOW:

texture LightsTexture;

sampler  ColorSampler  : register(s0);

sampler LightsSampler = sampler_state{
    Texture = <LightsTexture>;
};

struct VertexShaderOutput
{
    float4 Position : POSITION0;
    float2 TexCoord : TEXCOORD0;
};

float4 PixelShaderFunction(VertexShaderOutput input) : COLOR0
{
    float2 tex = input.TexCoord;

    float4 color = tex2D(ColorSampler, tex);
    float4 alpha = tex2D(LightsSampler, tex);

    return float4(color.r, color.g, color.b, alpha.r);
}

technique Technique1
{
    pass Pass1
    {
        PixelShader = compile ps_2_0 PixelShaderFunction();
    }
}