I am interested in knowing what the different indices used are to quantify biodiversity studies? Are there any free softwares that calculate such an index?
Addition to the above comments, I would like to pay your attention on two more biodiversity indices. They are Taxonomic diversity and Taxonomic distinctness which are proposed by Warwick and Clarke (1995). You can use PRIMER software to calculate those easily.
As many have advised, diversity indices are aplenty. However, they are not essentially 'biodiversity indices'. The indices are restricted to the diversity of the target group of organisms. And often it is some very restricted group like butterflies, spiders, trees, birds etc. Further, diversity is studied at 3 levels- alpha, beta and gamma. If you have access to Magurran's book, you will understand all the basic concepts and applications. If you want a quick glance at how it is applied, you can go through my paper on 'spider diversity attributes...'