ksa, переименовать забыл? Думаю, скорее так.
var a1=document.getElementsByName('field1[]');
var a2=document.getElementsByName('field2[]');
var a3=document.getElementsByName('field3[]');
<form>
<table>
<tr>
<td><input type="text" name="field1" value="1"></td>
<td><input type="text" name="field2" value="2"></td>
<td><input type="text" name="field3" value="3"></td>
</tr>
<tr>
<td><input type="text" name="field1" value="4"></td>
<td><input type="text" name="field2" value="5"></td>
<td><input type="text" name="field3" value="6"></td>
</tr>
<tr>
<td><input type="text" name="field1" value="7"></td>
<td><input type="text" name="field2" value="8"></td>
<td><input type="text" name="field3" value="9"></td>
</tr>
</table>
</form>
<script>
var a1=document.getElementsByName('field1');
var a2=document.getElementsByName('field2');
var a3=document.getElementsByName('field3');
alert(a1[0].value);
alert(a2[1].value);
alert(a3[2].value);
</script>