TL972: Single-rail & rail-to-rail?

Hi,

I have an application that requires a single +5V rail, and I need a non-inverting amplifier with a gain of 2 for an input range of about 0.1V < Vin < 2V. I chose a TL972 rail-to-rail op amp because the datasheet says it will work with +/- 2.5V rails with a swing of +/- 2.4V. I am attempting to use that range, shifted up to +5/GND instead of +2.5/-2.5, expecting that I can apply a dc input of 0.1V and get 0.2V out. I am using a basic non-inverting circuit, except the Vref is at ground instead of half way between the rails.

When the input falls below 1V, it clamps at about 1V. Digging deeper into the datasheet, I see the recommended Vicm is 1.15V above the low rail. Apparently there is a good reason for this because my dc input signal gets clamped around there. Can someone suggest another op amp part number that would satisfy the requirement as it is currently configured?

Thanks very much!

Edit: After posting, I dug around in the Art of Electronics to find that what I am looking for is a "ground sensing" op amp. The LM358 seems to be an appropriate choice, although the output appears to be limited on the high end to 1.5V below the top rail. Other suggestions are certainly still welcome.

Mike