Exhibit (a)(1)(E)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

Third Wave Technologies, Inc.

at

$11.25 Net Per Share

Pursuant to the Offer to Purchase

dated June 18, 2008

by

Thunder Tech Corp.

A direct wholly-owned subsidiary of

Hologic, Inc.

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF WEDNESDAY, JULY 16, 2008, UNLESS THE OFFER IS EXTENDED.

June 18, 2008

To Our Clients:

Enclosed for your consideration are the Offer to Purchase dated June 18, 2008 (the “Offer to Purchase”) and the related Letter of Transmittal (which, together with any amendments or supplements thereto, collectively constitute the “Offer”) in connection with the offer by Thunder Tech Corp. (“Purchaser”), a Delaware corporation, to purchase for cash all outstanding shares of common stock, par value $0.001 per share (collectively, the “Shares” and each, a “Share”), of Third Wave Technologies, Inc., a Delaware corporation (“Third Wave”), at a purchase price of $11.25 per Share, net to the seller in cash, without interest and less any required withholding taxes, upon the terms and subject to the conditions set forth in the Offer. The Purchaser is a wholly-owned subsidiary of Hologic, Inc., a Delaware corporation (“Hologic”).

Also enclosed is Third Wave’s Solicitation/Recommendation Statement on Schedule 14D-9.

WE (OR OUR NOMINEES) ARE THE HOLDER OF RECORD OF SHARES HELD BY US FOR YOUR ACCOUNT. A TENDER OF SUCH SHARES CAN BE MADE ONLY BY US AS THE HOLDER OF RECORD AND PURSUANT TO YOUR INSTRUCTIONS. THE LETTER OF TRANSMITTAL IS FURNISHED TO YOU FOR YOUR INFORMATION ONLY AND CANNOT BE USED TO TENDER SHARES FOR OUR ACCOUNT.

We request instructions as to whether you wish us to tender any or all of the Shares held by us for your account, upon the terms and subject to the conditions set forth in the Offer to Purchase and the Letter of Transmittal.

Your attention is directed to the following:

1. The purchase price offered by the Purchaser is $11.25 per Share, net to the seller in cash, without interest and less any required withholding taxes, upon the terms and subject to the conditions of the Offer to Purchase.

2. The Offer is being made for all outstanding Shares.

3. The board of directors of Third Wave has unanimously (i) determined that the Offer and the Merger (as defined below) are fair to and in the best interests of Third Wave’s stockholders, (ii) approved,

adopted and declared advisable the Merger Agreement (as defined below) and the transactions contemplated thereby, including the Offer, and (iii) recommended that holders of Shares accept the Offer and tender their Shares in the Offer and, if required by Delaware law, adopt the Merger Agreement.

4. The Offer is being made according to the Agreement and Plan of Merger, dated as of June 8, 2008 (the “Merger Agreement”), by and among Hologic, the Purchaser and Third Wave under which, following the completion of the Offer and the satisfaction or waiver of certain conditions, the Purchaser will be merged with and into Third Wave, with Third Wave surviving the merger as a direct wholly-owned subsidiary of Hologic (the “Merger”). As of the effective time of the Merger, each outstanding Share (other than Shares that are owned by Hologic, the Purchaser or any other wholly-owned subsidiary of Hologic or Shares owned by Third Wave or by its stockholders who are entitled to and properly exercise appraisal rights under Delaware law) will be converted into the right to receive the price per Share paid in the Offer in cash, without interest, as set forth in the Merger Agreement and described in the Offer to Purchase.

5. THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 12:00 MIDNIGHT, NEW YORK CITY TIME, AT THE END OF WEDNESDAY, JULY 16, 2008, UNLESS THE OFFER IS EXTENDED BY THE PURCHASER (AS EXTENDED, THE “EXPIRATION DATE”).

6. The Merger Agreement includes customary representations, warranties and covenants of Third Wave, Hologic and the Purchaser, as well as customary closing conditions. The closing conditions provide, among others that, the obligation of the Purchaser to purchase the Shares in the Offer is subject to (i) the satisfaction of a minimum condition that there has been validly tendered in the Offer and not withdrawn prior to the expiration of the Offer a number of Shares that together with the Shares then beneficially owned by Hologic and the Purchaser represents at least a majority of (x) all Shares then outstanding plus, at the election of Hologic, (y) (A) all Shares issuable upon the exercise of any options to acquire common stock of Third Wave that are vested or expected to become vested on or before the expiration of the Offer, (B) any outstanding warrants to acquire common stock of Third Wave, and (C) any other right to acquire common stock of Third Wave upon exercise or conversion thereof on or before the expiration of the Offer; (ii) certain of the representations and warranties of Third Wave continuing to be true and correct in all respects as of the expiration date of the Offer as though made on such date (except to the extent such representations and warranties are made as of a particular date) except where the failure to be so true and correct, individually or in the aggregate has not had, and would not reasonably be expected to have, a material adverse effect on Third Wave, and certain of the representations and warranties of Third Wave continuing to be true and correct in all material respects as of the expiration date of the Offer as though made on such date except to the extent such representations and warranties are made as of a particular date in which case such representations and warranties shall have been true and correct in all material respects on such date; (iii) Third Waive performing in all material respects it obligations and complying in all material respects with its covenants in each case in accordance with the Merger Agreement; (iv) no court or agency shall have issued a temporary restraining order, preliminary or permanent injunction or other judgment or order and no law has been enacted which prohibits, restrains or renders illegal the consummation of the Offer or the Merger, on and as of the expiration date of the Offer; (v) none of the following shall have occurred and be continuing (a) any general suspension of, or limitation on trading in securities on Nasdaq (other than a shortening of trading hours or any coordinated trading halt triggered solely as a result of a specified increase or decrease in a market index), (b) a declaration of a banking moratorium or any suspension of payments in respect of banks in the United States, (c) any material limitation (whether or not mandatory) by any governmental authority on the extension of credit by banks or other lending institutions, or (d) in the case of any of the foregoing existing at the time of commencement of the Offer, a material acceleration or worsening thereof; (vi) the expiration of the waiting period under the Hart-Scott-Rodino Antitrust Improvements Act and any other applicable federal, state or foreign antitrust laws, rules or regulations; and (vii) that no material adverse effect on Third Wave has occurred between the date of the Merger Agreement and prior to the expiration of the Offer. See Section 14—“Conditions of the Offer” of the Offer to Purchase for a description of the conditions to the Offer.

7. Tendering stockholders will not be obligated to pay brokerage fees or commissions to the Depositary (as defined below) or Innisfree M&A Incorporated, which is acting as the Information Agent for the Offer, or,

except as set forth in Instruction 6 of the Letter of Transmittal, transfer taxes on the purchase of Shares by the Purchaser in the Offer. However, U.S. federal income tax backup withholding (currently 28%) may be required unless an exemption applies and is provided to the Depositary or unless the required taxpayer identification information and certain other certifications are provided to the Depositary. See Instruction 8 of the Letter of Transmittal.

If you wish to have us tender any or all of your Shares, please so instruct us by completing, executing, detaching and returning to us the instruction form below. An envelope to return your instructions to us is enclosed. If you authorize the tender of your Shares, all such Shares will be tendered unless otherwise specified on the instruction form.

YOUR INSTRUCTIONS SHOULD BE FORWARDED TO US IN AMPLE TIME TO PERMIT US TO SUBMIT A TENDER ON YOUR BEHALF BY THE EXPIRATION DATE.

The Offer is not being made to, nor will tenders be accepted from or on behalf of, holders of Shares in any jurisdiction in which the making of the Offer or acceptance thereof would not be in compliance with the laws of such jurisdiction. However, the Purchaser may take such action as it deems necessary to make the Offer in any jurisdiction and extend the Offer to holders of such Shares in such jurisdiction.

Payment for Shares purchased pursuant to the Offer will in all cases be made only after timely receipt by Computershare Trust Company, N.A. (the “Depositary”) of (i) certificates representing the Shares tendered or timely confirmation of the book-entry transfer of such Shares into the account maintained by the Depositary at The Depository Trust Company (the “Book-Entry Transfer Facility”), pursuant to the procedures set forth in Section 3 of the Offer to Purchase, (ii) the Letter of Transmittal (or a facsimile thereof), properly completed and duly executed, with any required signature guarantees or an Agent’s Message (as defined in the Offer to Purchase), in connection with a book-entry delivery, and (iii) any other documents required by the Letter of Transmittal. Accordingly, payment may not be made to all tendering stockholders at the same time depending upon when certificates for or confirmations of book-entry transfer of such Shares into the Depositary’s account at the Book-Entry Transfer Facility are actually received by the Depositary.

UNDER NO CIRCUMSTANCES WILL INTEREST BE PAID ON THE PURCHASE PRICE OF THE SHARES TO BE PAID BY THE PURCHASER, REGARDLESS OF ANY EXTENSION OF THE OFFER OR ANY DELAY IN MAKING PAYMENT.

Instruction Form with Respect to

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

Third Wave Technologies, Inc.

by

Thunder Tech Corp.

A direct wholly-owned subsidiary of

Hologic, Inc.

The undersigned acknowledge(s) receipt of your letter and the enclosed Offer to Purchase dated June 18, 2008, and the related Letter of Transmittal, in connection with the offer by Thunder Tech Corp. to purchase all outstanding shares of common stock, par value $0.001 per share (the “Shares”) of Third Wave Technologies, Inc.

This will instruct you to tender the number of Shares indicated below held by you for the account of the undersigned, upon the terms and subject to the conditions set forth in the Offer to Purchase and the related Letter of Transmittal.

Number of Shares to be Tendered:                                                                                                                                                          

Account Number:                                                                                                                                                                                           

Dated:                                                                                                                                                                                                                 

* Unless otherwise indicated, we are authorized to tender all Shares held by us for your account.

PLEASE SIGN HERE

Signature(s):                                                                                                                                                                                                    

Name(s) (Please Print):                                                                                                                                                                                

Address:                                                                                                                                                                                                            

Zip Code:                                                                                                                                                                                                          

Area Code and Telephone No.:                                                                                                                                                                 

Tax Identification or Social Security No.:                                                                                                                                             

My Account Number With You:                                                                                                                                                              

Date: