Further Correction / Amplification: In the introductory paragraphs, this article states that VIX uses at-the-money options on SPX with 30-days to expiration. While the VIX does use options on SPX and while it includes only options with about 30 days to expiration, it appears to include a broader range of strikes now than in the past.
In the past, it used only at-the-money options as it was originally designed (see below). The following paragraphs by CBOE (the Chicago Board Options Exhange) explain this in more detail. (The CBOE would be the most authoritative source on this issue.)
"In 1993, the Chicago Board Options Exchange® (CBOE®) introduced the CBOE Volatility Index®, VIX®, which was originally designed to measure the market’s expectation of 30-
day volatility implied by at-the-money S&P 100® Index (OEX®) option prices. VIX soon became the premier benchmark for U.S. stock market volatility. It is regularly featured in
the Wall Street Journal, Barron’s and other leading financial publications, as well as business news shows on CNBC, Bloomberg TV and CNN/Money, where VIX is often
referred to as the “fear index.”
Ten years later in 2003, CBOE together with Goldman Sachs, updated the VIX to reflect a new way to measure expected volatility, one that continues to be widely used by financial
theorists, risk managers and volatility traders alike. The new VIX is based on the S&P 500® Index (SPXSM), the core index for U.S. equities, and estimates expected volatility by
averaging the weighted prices of SPX puts and calls over a wide range of strike prices. By supplying a script for replicating volatility exposure with a portfolio of SPX options, this new methodology transformed VIX from an abstract concept into a practical standard for trading and hedging volatility. "
Here is a very simple explanation (quoting Investopedia) on how VIX is calculated generally:
"VIX values are calculated using the Cboe-traded standard SPX options, which expire on the third Friday of each month, and the weekly SPX options, which expire on all other Fridays. Only SPX options are considered whose expiry period lies within more than 23 days and less than 37 days.
While the formula is mathematically complex, it theoretically works as follows: It estimates the expected volatility of the S&P 500 Index by aggregating the weighted prices of multiple SPX puts and calls over a wide range of strike prices.
All such qualifying options should have valid nonzero bid and ask prices that represent the market perception of which options’ strike prices will be hit by the underlying stocks during the remaining time to expiry."