June 18, 2008 Dear Third Wave Stockholder:

Exhibit (a)(2)(A)

June 18, 2008

Dear Third Wave Stockholder:

We are pleased to inform you that on June 8, 2008, Third Wave Technologies, Inc. (“Third Wave”) entered into an Agreement and Plan of Merger (the “Merger Agreement”) with Hologic, Inc. (“Hologic”) and Thunder Tech Corp. (“Purchaser”), a wholly-owned subsidiary of Hologic.

Under the terms of the Merger Agreement, Purchaser is commencing today a cash tender offer to purchase all of the outstanding shares of common stock, par value $0.001 per share, of Third Wave (the “Common Stock”) at a price of $11.25 per share, net to the seller thereof in cash, without interest thereon, less any required withholding taxes, upon the terms and subject to the conditions set forth in Purchaser’s Offer to Purchase, dated June 18, 2008, and related materials enclosed with this letter. Unless subsequently extended in accordance with its terms, the tender offer is currently scheduled to expire at midnight, New York City time, on July 16, 2008, at which time, if all conditions to the tender offer have been satisfied or waived, Purchaser will purchase all shares of Common Stock validly tendered pursuant to the tender offer and not properly withdrawn. Following the consummation of the tender offer, Purchaser will merge with and into Third Wave on the terms and subject to the conditions set forth in the Merger Agreement, and each share of Common Stock that is outstanding and that has not been accepted for purchase pursuant to the tender offer (other than shares of Common Stock that are held by (a) Purchaser, Hologic or Third Wave (or by any direct or indirect wholly-owned subsidiary of Hologic, Purchaser or Third Wave), which will be canceled and (b) stockholders, if any, who properly exercise their appraisal rights under Delaware law) will be converted into the right to receive cash in an amount equal to $11.25 per share.

The offer is subject to a number of terms and conditions more fully described in Purchaser’s Offer to Purchase accompanying this letter. These conditions include, among other things, there being validly tendered and not withdrawn before the expiration of the offer a number of shares of Common Stock of Third Wave, that, together with the shares of Common Stock then owned by Hologic and Purchaser (if any), and without giving effect to any shares of Common Stock held by Third Wave as treasury stock, represents more than fifty percent (50%) of the then outstanding aggregate number of shares of Common Stock, plus, at the election of Hologic, an additional number of shares of Common Stock up to, but not exceeding, the aggregate number of shares of Common Stock issuable upon the exercise of any outstanding option to purchase shares of Common Stock that is vested or is expected to become vested by its terms (other than by reason of the merger) on or before the expiration date of the offer, any warrant to purchase shares of Common Stock, or any other right to acquire shares of Common Stock upon exercise or conversion thereof on or before the expiration date of the offer including, without limitation, any shares of Common Stock issuable upon exercise of any restricted stock units of Third Wave or conversion of Third Wave’s outstanding convertible notes. Until the conditions to the offer are satisfied, or in certain circumstances waived, Purchaser will not be obligated to accept your shares of Common Stock in the offer.

After careful consideration, the board of directors of Third Wave has unanimously determined that the Merger Agreement and the transactions contemplated thereby, including the tender offer and the merger, are advisable, fair to and in the best interests of Third Wave’s stockholders and approved the Merger Agreement and the transactions contemplated thereby, including the tender offer and the merger, on the terms and subject to the conditions set forth therein. Accordingly, the board of directors of Third Wave unanimously recommends that holders of Common Stock accept the offer, tender their shares of Common Stock to Purchaser pursuant to the offer and, if required by Delaware law, vote their shares of Common Stock in favor of the adoption of the Merger Agreement in accordance with the applicable provisions of Delaware law.

In arriving at its recommendation, the board of directors of Third Wave gave careful consideration to a number of factors that are described in the Solicitation/Recommendation Statement on Schedule 14D-9 that accompanies this letter. Also accompanying this letter is a copy of Purchaser’s Offer to Purchase and related materials, including a letter of transmittal for use in tendering your shares of Common Stock to Purchaser in the tender offer. These documents set forth the terms and conditions of Purchaser’s tender offer and provide instructions as to how to tender your shares of Common Stock. We urge you to read and consider each of the enclosed materials carefully.

Very truly yours,

Xxxxx X. Xxxxxx

President and Chief Executive Officer

000 XXXXX XXXX XX XXXXXXX, XX 00000-1256 P: 608.273.8933 F: 608.273.8618 WEB: XXX.XXX.XXX